I would open an account with one of the online brokers - for example, IWeb Share Dealing.
Then you can set up regular payments in, and regular investments. Buying a stock or ETF this way costs you only 2 pounds a throw.
So each month you auto transfer in 100 pounds, and set your account to buy 100 pounds of VUKE (which is a low-cost FTSE 100 ETF, run by Vanguard).
You can also set dividends to automatically reinvest, though with ETFs you cannot buy fractional shares.
You could try HMCX which tracks the FTSE 250.
Reasons I say these two is that they are UK-based so you don't get currency risk. You could buy VXUS, I think, which is a really good US$ based Vanguard ETF that basically holds everything (except the US) - not sure you have access to NYSE stuff on the UK platforms though. I think you do not, by default.
I mean - ok, so the first question should be 'what is your goal for this money?'. If you want to use it soon then a cash ISA is the only thing to buy. Or perhaps some NS&I interest-rate following stuff - I don't know much about that (as I'm no longer in the UK). But if it's for long term, setting up monthly purchases like the above will take you far. As you get more money to invest you can add investments (Eg, European ETFs, real estate ETFs, and so on...).