It's always based on weight but if they are friendly at your local post office and you go at a quiet time of day (ie not lunchtime!) they would probably weight it for you and give you a quote. I've just sent two pairs of jeans to someone weighing 1.3kg and the cost for first class recorded delivery (you should choose some sort of tracked service) was £6.55 - this was the price for up to 2kg which might be enough for a fly rug.
Heavier rugs such as turnouts are horrendously expensive to send via Royal Mail, so I always use a courier, but again you need to know the weight.
Are you on a livery yard? You might find they have a spring balance to weigh haynets and these are usually accurate enough - pop the rug in a hay net or plastic bag to weigh it.
Unfortunately horses are at home, I work from home and nearest Post Office is 30 min drive away. I don't usually leave the property in the week! Will try and send husband out with the parcel to weigh on his way to work!
I have two turnouts for sale for £20 and £25 and the only responses I've had are from people who want me to mail them. Like, that's going to be a significant proportion of the asking price over again :-/ It's really more than I can be bothered doing (for the sake of twenty quid I'll hang on to them!) but I'm baffled by these people who want to pay postage. And slightly suspicious
If you jump on your scales with and then without your rug thatll give you the weight and then you can check online at the price comparison websites.
The flyrug I just sold was 5.5kilos as it had a waterproof bit so heavier. The cheapest was with Hermes about £7 I think. PO wanted £14ish.