I am planning to travel England in next December(20-27th). But my current Schengen visa is valid till December 31st. I am not sure, if my visa application will be refused because of that?I have not found any clear information in gov.uk site. They only mentioned, I need to have valid visa when I travel.
You want to apply for Standard Visitor Visa and you have a Schengen that will expire about two weeks after you arrive in the UK.
so my question is, is there any possibility to get refused to get British VISA considring my current situation?
Yes, those are delicate situations and they are not going to be happy about it. It looks like you want to remain in Europe after your Schengen expires and are using a UK visa as a pretext to advance a secondary agenda. Maybe you are, maybe you're not, but that's what they will think. They are paid to think like that.
They will also be wondering why you did not extend your Schengen and more importantly what is making you apply for a UK visa at this particular time (that can be a show-stopper). You need to get proactive and address both of those in your application BEFORE they have a chance to start worrying about it.
In a more general sense, they usually like it when the applicant has a Schengen currently or in their history. It means the applicant has already performed in a regulated environment (that's a good thing). But the timing of the application in your case is suspect and hence elevates the risk of refusal. So be diligent and proactive.