Is it legal ?

I am part of my sons "bubble" and I am fairly sure it is OK to have them for a birthday meal. How I read it was that you are classed as part of their family bubble. Have a nice meal!

Not worth the risk

Did Captain/Major Tom get covid from his bubble? I don’t know if he did or didn’t but be careful.

It is legal, and if you are seeing just the same people as you’re seeing regularly in your home anyway, I don’t see how it’s putting you at more risk.

To be honest I think you are putting yourself at risk whether it is allowed or not. Can’t the birthday party be postponed until another time?

Putting aside what is legal have you considered what is sensible?
You are the one at risk in this scenario. Bubbles don’t protect you from coronavirus, outside contact could result in you being hospitalised. Having anyone come into your home is dangerous.
With light at the end of the tunnel why would you want to risk it now?

I'm pretty sure that if you are in their bubble, then you are treated as part of that family group.
I'm can't see why you shouldn't have them to a meal.