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The first place I recommended was bespoke funnily enough! Have only been for a £100 "intro bikefit" ages ago but they really impressed me.
Thought that should be the sort of company with his budget/style of riding. He's in hampshire but I reckon he'll come up here for it.
Vesalius-
The helpful advice you're getting in the road bike thread is the exact reason I did what I did.
You definitely shouldn't listen to me, I had a 3k road bike budget with no idea what I wanted, so my eventual purchase was evidently a terrible, terrible mistake. I'm 5'4" tall with 700c instead of 650b on all my bikes, and I have a 29er even though obviously it's so small that the geometry makes it completely unrideable, and I use rear racks instead of front racks, and I also use spacers/don't use spacers on my headsets, and rim brakes instead of whatever else it is I'm supposed to be using to make my bikes usable. I'm very happy with all of my bikes, but, y'know. I'm deluded. And clueless. With bikes that don't work and that are uncomfortable. I've imagined all the many, many, comfortable and happy miles I've ridden, I guess.
bothwell
When I got my road bike I knew fuck all about road bikes, so the way I did it was to go to Bespoke Cycling in Farringdon, have them give me a bike fit, then tell me what they recommended from their own stock based on my fit and budget. Then I bought one of the bikes they recommended from them, and had them do the final adjustments. Totally hassle-free and I'm still very happy with the bike and the general experience. If he's in London then I would totally recommend he do that, even down to using the same shop, tbh.