Halifax vs Nationwide Mortgage

Hello,

I'm trying to buy a Shared Ownership House which costs £125,000 for a 60% share and initially went with Halifax but the valuation has come back saying its only worth £112,000 for the 60% share an so won't offer me a mortgage on the original terms.
This valuation is obviously wrong as another house across the road sold recently (within 6 months) for £102,500 for a 50% share and this has a much smaller garden. So this means a price of £205,000 total compared to £208,333 for the one i'm buying. I've tried to appeal it but the surveyor says the valuation has something to do with Halifax's valuation rules and as this is the only similar house that sold in the last 6 months in my area (it's very rural) then there is nothing else i can do.

The other house has a mortgage with Nationwide and their valuation went through without problem. Do they value in a different way? and would it be ok for me to apply with them even though i have tried Halifax first? (as they have left a search on my report).

Thanks for a any help.