I have a high 2:1 B.Sc. in maths (close to first class) and I have been offered a place to study M.Sc. in applied maths in Imperial and UCL.. The year after my masters I want to start phd studies..
Also my masters' exam period is during the third academic term and consequently a few months after the dates I will have to submit a Phd application.
As a result, I won't be able to present any graduate level results in my application.

In this case, do you think I might encounter problems because of my B.Sc. grade?
I think it might be weak for these universities.. ( or others in Uk top 10-15)
Also, will I have a problem with the funding ? Is it possible to find adequate money for 3-4 years? Does anyone have experience in respective situation?

Thanks in advance.. any thoughts are welcome

Many people end up applying for PhDs prior to completing their MScs, this is quite normal.

What usually happens is your MSc supervisors will provide you with a reference which comments on your academic ability and predicts a grade. Usually, your offer of a PHD place (and/or funding) will be conditional upon you achieving a certain grade in your MSc (which might be a pass or a merit, depending on both the institution you are studying and at the one you are applying to).

I got PhD funding with a mid-2.i in my undergrad because my supervisors at MSc level saw I was getting distinction grades consistently in my MSc - it was more closely related to the subject I Wanted to take at PHD than my u/g so I did better in it. It definitely helped that I was applying for PhDs at the same place as my MSc though.

Had you taken any masters level exams when you applied for the phd?

I'd had some marks back for a couple of modules, which were at distinction level. But, my referees knew me quite well because I always contributed in class and demonstrated that I had a brain, which definitely helped.

If you're MSc referee is only commenting on your marks, then I suspect you are in trouble. They should definitely know you and your capability to think at this point (assuming you starting in Sept).

thank you very much!!

My experience was similar to IntoTheSpiral's - I'm in a different field, but got my PhD offer with partial MSc results (distinction grade) and references which stated I was capable of independent study. I wasn't asked for my final MSc grade at any stage (even after starting the PhD).