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Can't see why they'd care, you'd just need to tell them why. There's nothing stopping you selling a house for £1. It wouldn't be much different to you providing £100k against a FMV of £300k.
The fair market value of the property will be used as far as CGT/IHT is concerned, but that shouldn't affect getting a mortgage on the property, and CGT shouldn't affect you, IHT might but depends on the circumstances.
Assuming we wanted to buy a property from someone who agreed to sell it to us at less than market value would banks be shitty about that from a mortgage perspective?
Say value is 300k and prospective sale price is 240k. Say we had 40k savings plus stamp duty/legal costs and wanted a mortgage of 200k. Would we be OK getting that full 200 or would they question it because of the market value of the property?