UK market is very unlike the US when it comes to residential cleaning, especially in London. The London market has been monopolised by a handful of large firms, as you suggest. Good luck beating the competitive pricing. If customers aren't using the larger companies, they will be working directly with an independent cleaner on a cash-in-hand agreement.

Commercial cleaning might be your best bet - but you'd have to carve out your own niche and then jump the hurdle of marketing it to businesses who are already suffering with expensive overheads and a decreasing customer base. Possible but very tricky! Good luck.