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LTV on current deal is about 25% on 1.7% fixed for 2 years
To expand on the earlier answer. Partner just got a 2nd mortgage on her place to do an extension. The bank will go through the same affordability chats with you that they did for the first one, and they'll revalue the house (this may just mean they look on Google Maps to see if it's probably still there, they look at the Zoopla valuation).
Assuming they think there's enough headroom in the current valuation then they'll offer based on that. So it shouldn't really work out too differently to the first in terms of how it works, you'll just end up having two payments a month instead of one.
Depends on what % your current mortgage is, I'd have thought, ie is there enough equity in house to balance against the 2nd mortgage?
If the bank have suggested a second mortgage, I presume there is.