Winter Road Clothes on a budget

Hi All

I’m looking for some suggestions to kit out my winter riding kit on a bit of a budget

So what i have currently is

Base Layer (not a full winter job just a synthetic type fabric, similar to a compression base layer)

Short Sleave Summer Jersey

Summer Arm Warmers

Nitebrite Full waterproof Jacket

Summer Shorts

Winter Socks

Now as you can imagine on these british winter days it’s getting far too cold for this, layering up is fine BUT living at the top of a steep hill the Jacket which keeps me relatively warm on the flat becomes a burden and i am sweating buckets.

Now with Christmas fast approaching i have an oppertunity to spend a little to get some good winter/Autumn kit, im set for rain gear need warmth more than anything.

Looking for some real suggestions in the £30 – £50 range that will be an effective way of warming up for rides.

Worth noting that for a commute i ride about 15 miles a day but am often doing longer rides although usually when it has warmed slightly.

Any suggestions or assistance for utilizing what i already have along with some new items is greatly appreciated.

My thoughts were some long tights, a winter jersey (although not sure if worthwhile with the baselayer as well as summer jersey combo), maybe a windproof jacket etc.

I will be looking at spending more after Christmas however don’t want to have to stop riding until then.

Thanks in advance

Neil