Hi all, thanks for your comments, and thanks for confirming the tree doesn't need to be cut down: very much appreciated.
Gary: indeed the wall is cracking due to the roots pushing up. The pavement is also heaving up, and it's one of the reasons for my post. I have been getting quotes to rebuild the wall with a gap to allow further root growth but since they're quoting £500 upwards I thought I'd check if the tree was going to come down soon after. (Then we don't need to leave out bricks.)
I hadn't heard about included barks . I will have to find someone to view it.
openspaceman: I wasn't aware of the type of oak it was , thanks for pointing it out. Pity it's not native, but I don't think that's a reason to give it the chop. I can't quite work out your comments about "militates against retention in my book" ..?
Gary: The tree is great, we get some privacy in the front bedroom from the neighbours across the street and in general my wife and I like trees (WIFE: "I'm sick and tired of people cutting down trees"). Pity its not native but if I replace it with something native I'll have to wait a few decades before it's grown again so we'll just keep this as long as we can.
Unfortunately, there was a magnificent tree a few doors down (everyone commented on it), if I'm remembering correctly, it was the same company that suggested my tree should come out which diagnosed that tree as being unsafe. It got some "keep clear" signs on it one day and was gone 2 days later.. The owner was upset but felt they had no option due to the risk.
Paul: reducing height I have no problem with. This is not the country side to allow the tree to grow unrestrained. I have 3 of those in my back garden and 2 next door leaning into my property. Same guy was quoting £500-800 per tree for those: these lovely garden trees are costly.!
Bracing / cabling: that might not look pretty but sounds a good idea.
thanks again,
Hadyn