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Play with this... https://www.zoopla.co.uk/travel-time/
It's not perfect and is not set up for cycling but you can fiddle with it to try to find an area.
dst2-
There is one for cycling somewhere, I'll see if I can dig it out...
Found it - https://www.findproperly.co.uk/faster-by-public-transport-or-bike.php#.WbpNlP6ouUk - looks like it only does bus and tube, not trains, as I'm fairly sure that train to CLJ or VIC is faster than cycling there for me...
MrDrem
I'm not living in Victoria!
Not sure on the budget, a flat in my block which is smaller than mine just went on sale for £475k, if it makes that then I'm going to have to reconsider what I think mine will make.
We have £300k equity from the current place, and I could (from a brief play with the HSBC calculator) get a mortgage for 600K, although the prospect of that has me frankly terrified.
With some more work on the HSBC site, picking a value of £750k gives a monthly repayment of £1,694 which is ok, so lets pick that as the ceiling price.