I've read other answers but they haven't been specific to my problem. I have a 8 month old female spayed beagle. She has just started to wet herself in her sleep both at night time and during the day. Can anyone help me by telling me how to help her to stop?

It sounds like she may have spay incontinence.
I am unsure of the complete specifics but I believe that after spaying the b*tch has trouble controlling the muscles that keep urine in her bladder while she is relaxed.

You need to make an appointment with your vet to make sure it is not an infection and that is is incontinence and he will instruct you where to go from there.
There are drugs available to ease the problem, if you decide to go against the drugs come back and I will give you some tips on keeping your house and bedding from smelling as I have a b*tch with the same problem and I do not use the drugs.

I forgot to say that before this she has been wetting herself when she gets very excited- like every time my mum comes home and has now just started to do it in her sleep.

The urinating whe nshe is excited could well be a different problem/
Some dogs lose bladder control when they are excited. There are ways to fix it such as when you (or your mum) comes home you need to ignore the dog, don't show her any attention until she has calmed down.
After a week or so she should not get so excited when you come through the door and it will help with the urinating.

Thanks I'll try that anyway.