I used to own an iRobot Roomba 560. It cleans really well but you have to give it some time to "learn" the layout of your house. The battery life is good as well. It can finish my living room and kitchen and the docks back to charge.
The drawback I felt was that it was loud and it will bang into chairs. So before each run, I have to put up the dining chairs on the table and move the computer chair into one of the rooms.
I bought my machine from the states via Amazon and VPost. That arrangement was cheaper compared to buying directly from the Singapore distributor. The only disadvantage about this is that you have to buy and adapter as US is using a different plug and there's no warranty.
Now with the GBP going so low, you might want to explore Amazon UK to see if they carry the iRobot.
All in all plus shipping I paid not more than $700 or $800, I can't remember. Bought it a while ago.