There are many different considerations the lender look at when deciding how much they will lend you. One being what is called loan to value. e.g. value £100k loan £95k = 95% loan to value
Most mortgages have a max. LTV and it is depending on your rate, eg lower rate for lower LTV
If the property is worth £100k and you are buying half for £50k, and you wish to borrow £50k then your LTV is effectively 100% from the lenders perspective, if the prop is down valued by £5000 but you are still paying the asking price the lenders will only lend you 100% of £47500
i hope this helps.
Tenacious T
I am a financial adviser but am here only to point peeps in the right directions, most of the time this will be to speak to an IFA, we are not monsters and charges are agreeable upfront so dont be afraid, pick up the phone