This section is not specific to Essex maps, but rather applies to all maps.
Listed below are dozens of map dealers, mainly of antique maps, but also some who specialise in Ordnance Survey maps. I have no affiliation or link with any of these, and I am not endorsing them in any way, but I can say I have used several of them and have always found them very helpful and fast to respond.
After map dealers I have listed auction houses that hold regular auctions that have material numbers of maps and/or atlases.
ABE Maps is the "fixed sale gallery" of Paulus Swaen, who's main business is the Auction site (listed below)
Albion Prints have a great deal of prints and some maps.
Altea Gallery A major london gallery, although their website bunches counties together in random order that makes it harder to browse. They have a dealer shop in London.
Antiqua Print Gallery is mostly for prints, but some maps. They have premises in London.
Antique Map Shop Ltd A website-only dealer, although not many maps of Essex.
Antique maps & Prints A major website-only dealer.
Antique Maps Online.co.uk A large website-only dealer, although not many maps of Essex.
Antique Print Club An Australian website, so not too many English maps.
Antique Maps.com A very major website-only dealer, with a very large stock and lots of additional information.
Antique-Prints-Maps A major website-only dealer, with a very large stock.
Ashrare Books Primarily a dealer in rare books, the website also has some county maps and a lot of prints. The owner, Laurence Worms, is the major authority on map engravers in England.
Barry Lawrence Ruderman Located in California this is a good site for very old international maps, but not great for English counties.
(Roger) Baynton-Williams Gallery The site has all the options for maps and prints, but not a large stock.
Bryars & Bryars A West End dealer (closeby Storeys Ltd) with a large stock of county (& other) maps.
CA Burden An excellent dealer for maps, but is the absolute top dealer if you want whole atlases - the stock of atlases (& maps) is huge.
Copperplate A major website-only dealer, with a very large stock (especially for Cambridgeshire and adjacent counties).
Cumbria maps A small website-only dealer, specialising in north-west England and adjacent counties.
Crouch Rare Books A high-end West End dealer, specialising in the more expensive items - maps and atlases.
Furneux Antique Maps A major website-only dealer, with a very large stock.
Garwood & Voigt A major dealer based in Sevenoaks Kent, with a very large stock.
Gillmark Gallery has a huge stock of Hertfordshire maps in particular, plus all other counties, etc. Sadly it has moved from Hertford to Yorkshire, but still provides an excellent website.
Heatons A dealer in Tisbury, Wiltshire, with a very large number of prints and some maps.
InterCol A London dealer of many topics, with some maps.
Jonathan Potter Maps A large stock of maps, now based in Bath.
Kevin Ryan A web-based dealer, who as well as having an internet business creates half-hour TV podcasts available on his site.
Kings Antiquarian The website for print and map sales of two country dealer shops - in Dorchester and Lyndhurst.
Kings Court Gallery A very large shop at the Putney end of the Fulham Road in London, with a very large stock of maps.
Kitty Liebreich There doesn't appear to be much stock on the website, and I think works mainly by finding items for clients.
Laurence Oxley A dealer in Hampshire, based in a shop selling many things including maps. Does not have pictures of the maps on the website.
Lee Jackson A website-only dealer based in London.
Lesley Aitchison A dealer in Bristol who specialises in local history, particularly in Acts of Parliament. They have some maps and many other interesting items.
Lindisfarne Prints A website-only dealer with no stated address, but a Shrewsbury phone number.
London Map Gallery A website-only dealer accessed via eBay.
The Map House A very large West End dealer, with a large stock of maps, but no prices shown
Map Mogul A website-only dealer based in London.
Map World A dealer with a shop in Canterbury, with many maps on the website, particularly international ones - but apparently no county maps.
Maps Perhaps A website-only dealer based in Tetsworth (Oxfordshire).
Miklian Antiquarian Maps A website-only dealer based in Jackonsonville, Florida.
Mostly Maps A dealer with a shop in Hay-on-Wye, with a good stock of county (& other) maps on the website.
Old Maps.com Not a dealer, but rather a company that provides a voluminous list of map prices as a subscription on-line service.
The Old Map Man A website-only dealer with a good stock of county (& other) maps.
Paralos An Athens based dealer who is obviously strong on Greek maps, plus some from around the world.
Past Pages A website-only dealer from Kent that has a large stock of county (& other) maps.
Philip Sharpe Gallery A web-based dealer who exhibits at several fairs.
Prints Old & Rare An American website-only dealer, that says they only put a "small selection" of their "huge inventory" on the website, so you may not find anything.
Puddletown Bookshop is a bookshop, but they do have some Atlases and map related books.
Rediiwi A web-based dealer based in Gloucester, with a particularly large stock of Pacific maps.
Robert Frew A West End dealer with a large stock.
Roderick M Barron is a map dealer, but specialising in imaginary, comic, satirical, propogandist and pictorial cartography.
Sanders of Oxford An Oxford dealer with a large stock of maps and prints.
Simon Hunter (Antiquemaps.org.uk) A website-only dealer that has a large stock of county (& other) maps.
Steve Bartrick A website-only dealer that has a large stock of county (& other) maps.
Storeys Ltd A West End dealer (closeby Bryars & Bryars) with a large stock of county (& other) maps.
Tooley Adams A website-only dealer that has a large stock of county (& other) maps.
Virtual Book Fair is a multi-dealer site (or "Fair"), operating for most (but not all) of the year.
Warwick Leadley A London dealer based in Greenwich.
Welland Antique maps A website-only dealer that has a large stock of county (& other) maps.
Antique Maps Fair is a specialist site selling maps and atlases at auctions 5 or 6 times a year (I think).
Bonhams, one of London's major Auctions Houses, sometimes has Atlases and (less often) Maps for sale.
Cheffins, a general auction house in Cambridge that has Atlases & Maps about twice a year.
Christies, one of London's major Auctions Houses, sometimes has Atlases and (less often) Maps for sale.
Dominic Winter is a specialist site selling maps and atlases at auctions 6 or more times a year; this is the major auction house for maps in the UK.
Old World Auctions is a specialist site selling maps and atlases at auctions 3 or 4 times a year.
Paulus Swaen is a specialist site selling maps and atlases at auctions 3 or 4 times a year.
Sothebys, one of London's major Auctions Houses, sometimes has Atlases and (less often) Maps for sale.