If it was me I would want more proof that the HG had gone.
My P reg Astra suffers a lot of sludge under the cap due to overcooling, but the HG has not gone.
I am not a mechanic or an expert but I would ask myself the following:
Is the oil on the dipstick black or milky? If its milky it has water in it, confirming HG failure
Is the oil level rising? This would suggest water is getting in, but if it is not rising that doesn't disprove the failure as the water may be going straight down the exhaust.
Are you losing water. If not I would doubt the HG going.
Do you have starting or running problems, particularly rough running where one cylinder is not firing. This would tend to confirm HG failure.
If the symptoms suggest just a small leak I would get myself down to Partco or a good car parts shop and ask for a bottle of their best leak stopper. This would not work in a serious case, and probably won't at all but I suggest it is worth trying.
If I am shot down in flames by more knowledgable people I put my hands up now.