I thought this thread needed a bump, so here is an account of what passes for coin shops in South-East England (Kent and Sussex).

This area has a lot of seaside towns with tea shops, fish and chip shops and antique shops, but relatively few coin shops, although there were more back in the 1980s. Going south from London, Brighton has a very quaint district called The Lanes. Here you'll find plenty of jewelry stores but no real coin shop. However, many jewelry stores have a few gold coins in the window that can be bought for a little over melt, and these can be worth checking as the shopkeeper will be more interested in the gold content than in the date or mintmark on the coins.

The North Laine district is full of trendy boutiques, hipsters, street art and passers-by wearing weird clothing. One of its main streets is Kensington Gardens, where there is a large indoor Antiques Market that has a stall with a few coins. But the best place to buy coins in Brighton is "Coastal Stamp Auctions", on the main road leading to the train station.

Despite its name, it specialises in coins, stamps and diecast model buses! The coins are fairly priced and there is usually a good selection of milled British coinage from Victoria onwards, with some quite nice foreign silver and some cheap rummage trays.
Heading east along the coast the next interesting shop is in Eastbourne, again near the train station. It's a collectors market with one serious coin dealer inside. He usually has a good range of milled British coins and a few foreign coins, plus various modern commemoratives and proofs. Unfortunately they are rather poorly displayed in a cabinet so you'll have to ask the dealer to unlock it and take out the coins individually to examine them.

Hastings, a little further along the coast, has two interesting shops in the High Street. Unlike most towns, the High Street in Hastings is very quiet and mostly residential, as it ceased being the town's main thoroughfare in the 1850s when a new business district opened around the train station. The first shop, the misleadingly-named "Antiques Warehouse", is at the southern end of the street, a stone's throw from the beach. The Duke of Wellington once stayed in this building while inspecting his troops at Hastings! It has several great rummage trays - all with 4 coins for £1. They are filled with pre-decimal British coins, pre-Euro EU coins and all kinds of other foreign coins. Apart from the trays, there are lots of campaign medals, some recent UK Proof and Mint Sets (fairly priced) and a few large silver foreign coins like Morgan and
Peace dollars (mostly overpriced).

On the opposite side of the street, walking inland, is "Robert's Rummage" (no connection to me!). This is a junk shop that usually has two coin trays, one with common UK pre-decmal pennies and halfpennies for 10p each, and another with mostly foreign coins for 25p each. I've found a few bargains here in the past, but the trays vary in quality depending on when the dealer last filled them up!

A few miles north of Hastings, on the actual site of the Battle of Hastings, is the small town of Battle. To the right of the entrance to Battle Abbey, in a quaint old building, is a shop called "Ancient Coins". The dealer specialises in Greek, Roman and hammered coins and has a large selection, plus quite a few recent
Royal Mint proof sets. He will also sell you Uncirculated 2016 Battle of Hastings 50p coins for the princely sum of £5. I think all his coins are a bit on the pricey side, but you could always try bargaining...

Rye, east of Hastings, is a very pretty little town that lost its last coin shop (located appropriately in Mint Street, site of the Saxon mint) quite recently. It has numerous antique shops where you'll probably find a few overpriced Victorian crowns and saucers containing pre-decimal British coppers. But the most interesting place for the numismatically-inclined visitor is the tourist office that houses a large model of the town with a sound-and-light show and a museum of vintage penny arcade machines, which operate with pre-decimal pennies. To obtain the coins to work the machines, you need to put a current £1 coin into the change machine on the wall, which will give you seven old pennies! I bet they don't check them for rare dates...

Moving on from Rye across Romney Marsh, the town of Hythe has a nice Antiques Centre in an old 18th-century brewery building called the Malt House Arcade. It's only open on Fridays, Saturdays and Bank Holiday Mondays, but it has quite a good coin stall manned by a knowledgeable dealer called Colin, who has a great rummage tray (4 coins for 25p) in addition to some more expensive (mostly British) coins under the counter.