The good news is at least now the initial 'desk survey' quotation for FTTP is free. There's a lot of rumor and conjecture floating around at the moment given that as far as i've seen no one has had the initial desk survey quotation back yet on the new system. However, it sounds like initial build costs will be higher to offset the lower ongoing pricing and contract lengths of the service itself.
Information on where exactly the aggregation nodes isn't exactly public knowledge,
again it's rumour and conjecture but i've seen it suggested that they may be likely to be located in places where there's two or three of the BTOR manhole covers in a row. I don't know if you're able to have a poke around on Street View and see what size the manhole covers are like near those cabinets you've identified, that may at least help you have a guess where there aggregation node possibly is and thus what the distance may be. Edit: Not necessarily correct.
Ultimately though, given the initial desk survey is now free you might as well request a quotation for build costs to your new property which will give you a much more exact figure than guesstimating on the line length from a possible aggregation node
I personally have requested a desk survey quote, back before I was able to get my line in a healthier state with the help of folks here and as an exercise in curiosity as to what even faster broadband might set me back (if the costs come back not too bad, I think even with a good FTTC line I might be quite tempted!). Given the lack of information out there at the moment I was planning on sharing what the quote came back with to help others here to help folks get an idea of what things are roughly like under the new scheme. It was just over a week ago that I put the quote in, so hopefully i'll hear back sometime this week.