Mortgage Interest Relief on rental income

I'm thinking of renting out my home and purchasing a new one.

My current house will be mortgage free but I need a mortgage to buy the 2nd house.

If I just take out a 2nd mortgage for the new house, I can't get Mortgage Interest Relief on the rental, as there is no mortgage on it.

However, if I re-mortgage my current house to buy the new one, can I then claim Mortgage Interest Relief when I rent it out?

Hope this makes sense!

No, it's the purpose the money was used for that is important and not which property it is secured on. As the money will not be for the rental property then you couldn't get interest relief on it.