I have a Chinese Elm, Ulmus Parvifloia Seiju, which got shocked in the hot weather this summer and dropped all it leaves.
They have started to grow back, but should I bring it indoors this winter?
I'm worried if it drops it's leaves in the winter, new buds may not have had time to from.
Any advice is greatly appreciated.

It got shocked by not having enough water. No leave it outside, it will be worse off inside. 

I think that your location and climate is important information to give a proper answer.

Geoff is in UK and his recomendation is based on his experience in that climate.

I am in Sweden, where chinese elms are not totally hardy. I keep my best elms in frost free overwintering room. Some spend the winter in unheated greenhouse. I have lost one this way, that is why I babying my best trees in the overwintering room.

Indoors in livingroom conditions is never an option wherever you are.

I agree with what you say, location is important, but I have had Chinese Elms down to -10C (in the past) with no problem. Not my smaller ones and not for many years as we don't get much below -5C and that rarely.

The year I lost my nicest elm was below -10 for 6 weeks straight day and night. Lowest was -18. That was extream to my area. Like once every 15 years or so.

I live in North West England, so extreme cold is rare as you say.
Normally I would leave it outside with no worries.
I'm just a little concerned with the new leaf just emerging that new buds will no form when the leaves fall.
Maybe I should just protect it from the frost?

If you have means to protect it from frost it does not hurt for sure. 5 degree overwintering room is the best. But a frost protected shed or coldframe can work as well.

Cold frame it is then.
thanks for the advice.

You need to be careful, as sunshine can push the temperature high, especially in spring and can cause early growth when it is not wanted. I would not put it in until there have been frosts, which here is late October.