From London, your best bet for weekend diving is the south coast - generally speaking the further west you go the better the visibility. There are loads of boats, some better than others going out from the various ports - Littlehampton, Poole, Weymouth, Falmouth, Plymouth are all good sites with wrecks in most depths from novice 20m stuff to deep gas diving.
One big difference is the boats always take a max of 12 divers, and many of the good boats get booked up a year in advance - so plan ahead, or you won't get where you want to be. There aren't as many 'open' boats, so it may pay to join a club/group until you get to know people or boats ( or they geet to know you, in which case more possibilities open up) There almost certainly won't be any kind of DM, you'll be expected to sort yourself out, and be up to the dive you've booked for - no one will check you out.
Also, much diving is square profile, rather than shallow/multi-depth, so minor decompression is the norm, longer decompression to uncommon. As such, the boats stay free, and most divers will bag-off from either the wreck or half way up.
I live in the very northern most bit of Scotland, and my opinion is the diving in Scotland is superb, but it is a long way from London. Worth diving the Farnes, Clyde ( expect low vis here) Moray Firth, Caithness, St Abbs, Oban etc etc - but from London go for a week
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