You don't need to be sick with worry. There is no evidence of subsidence at this point, just a fear that there is. So ease your mind and go ahead with putting it on the market without paralysing yourself with fear.
I've dealt with subsidence so I know that there are risks from trees' proximity to buildings and there are things you look for as signs of subsidence, if you suspect it.
Apart from obvious visible sinking or wonkiness in levels or angles of walls or floors when you look at the building, the things to look for are cracks in the walls of the building, in brickwork or internal walls, often vertical cracks around windows or doors or cracks between the ceilings and the walls or walls and floors.
Whether cracks are from subsidence or just normal settlement cracks that occur in new buildings is determined by a surveyor monitoring and measuring the cracks over time to see if they are getting any wider. This would normally take a period of several months at least and might be 18 months or more.
Even if there are cracks in the tarmac, it doesn't mean that the tree's roots have gone very deep or that nothing can be done to alleviate any risk of future subsidence.
The tree could be reduced in height - crown reduction - and root pruning is also a possibility. BUT you need a specialist arboriculturalist to assess and advise on these or other potential remedies. (You can't just cut down a tree, as that could cause a problem known as heave, the opposite of subsidence, which would affect the building and its foundations, causing cracks.)
And even if you had subsidence, it's not necessarily a disaster - it might be that if it was minor and not progressive, all you would need is to have the cracks in walls internal and external filled in, with resin bonding, for example, and take remedial action to the tree to prevent any further effects on the ground and foundations.