Two Mortgage Applications a Bad Idea?

Shanghai

I currently live and work abroad but am looking to buy a property in the UK. I work for a UK company but anyone who is in a slightly unusual position, such as me, seems to find it hard to get a mortgage these days.

I have a broker who has done some work and thinks that it is possible that he has found me a sypathetic lender. In the meantime I have contacted my own bank (HSBC), who has indicated that it is likely they can give me a mortgage (My broker doesn't have access to HSBC mortgages).

I am under a bit of time pressure in that I have to leave the UK shortly. Is it a bad idea to apply for mortgages at the same time through both my broker and through HSBC. If I get offered one and not the other it is simple. If I get offered both then I need to make a decision. If I get offered neither...

Will it create any problems to appy for two simultaneously (eg credit searches)?