Hello,
It depends on the mortage. Will it be a mortgage for your parents? In that case it shouldn't matter about your mortgage. It is more about their ability to get a mortgage of their own.

You could also get a buy-to-let mortgage (which is not taking into account your existing mortgage, but rather the potential rent you can get from letting the property out) and rent it out to your parents?

I would recommend that you contact a mortgage adivsor.

 

Well then in that case there is no much problem.
They have plenty of foreign investors buying properties in London at preposterous prices...