Maths phd in UK

[v2gls]

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)
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 a respective situation?

Thanks in advance.. any thoughts are welcome

Edited February 9, 2016 by v2gls

[Feanor]

That's the typical situation and they'd just make you an offer conditional to a certain performance in your Masters. Funding is always a more complicated matter, but it's significantly easier if you are an UK/EU student.