Thank you for your comments. It makes this world much easier! Any advice in High Brooms area? As houses seem to be slightly cheaper than TW?
I used to live a mile from HB station (toward TW) and the commute to Cannon Street was quite acceptable, I'd be a bit more reluctant to commute to the Wharf.
One thing to note is that there is a shuttle bus that goes to the Wharf from TW (has several stops), which once you factor in changes etc, might be quicker than the train and quite exclusive as it just picks people up around here and then drives straight there. That depends on your hours of course, but the people I've spoken to that have done it all perform metro roles.
HB is cheaper for a reason, but as long as you look at the quadrant of it that's west of the station you'll be fine. North is meant to be ok but a few of the places I looked at felt a bit more cramped and on top of each other. South and East of the station is a no go as far as I'm concerned.
The other option to consider are stations along from TW. It's a bit more of a commute but if you're only in the office 2 days per week it might be more acceptable, I've not been into the city for nearly a year now but HB was always touch and go whether you'd get a seat on the train. If you got on at TW you'd be guaranteed a seat no problem. The towns further south (Wadhurst & Frant really) are both nice too.
One last consideration, not something I've done many times from TW as my work doesn't have many parking opportunities nearby, is to get a motorcycle and commute that way. The South East trains are not cheap (think £40-50 per day without a railcard) and you might have better parking available in the Wharf.. This lets you look further afield than the station towns and you can get a lot more for your money that way.