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Yeah I can see why you are drawn to that, its bloody fantastic.
I've done various commutes work wise, longest was from Southampton to Dorchester which is roughly what you are talking but I was close to the station.
As others have said the 3 miles ride is going to be what gets you, one other thing thats worth mentioning IMO is that (I think) interest rates are only going to go up, meaning mortgage repayments are only going to go up. I would be nervous about stretching myself financially at this point in time, but this just me, I'm quite risk adverse.
This is good info. Yeah the 3 mile trip from the house to the train station is the bit I don't like. The other option would be drive to station and tube other end and then train home together in the evening.
https://www.rightmove.co.uk/property-for-sale/property-66048801.html
This is the house btw.