I love my budgies to bits, but they're rather boring.

I'd like to get a parrot so I can get the compassion that neither of my budgies give me.

Is it OK to mix them?

I would say no.

Apart from a parrot being a possible danger to budgies if its aggressive, their needs are very different ( housing / food requirements etc) and if one has an illness, it could pass that illness onto the other.

A parrot requires more money, time and attention than a budgie, so make sure you learn about owning one before making that final decision and one last thing - some parrots can create a lot of noise, of the ear splitting type, so you need to be aware of that too.

Budgies tend to only like cocketiels as they share a habitat in the wild. However, there is no saying this is always the case.

I agree with this, when I had a cockatiel I got him a little budgie friend and they loved playing and talking with each other. Cockatiels are very smart and cute birds and make good companions.

Did you not think about this before getting them ?

My advise would be to pass the budgies onto somebody who actually wants them and to steer clear of all pets in the future