This morning while doing a routine check under the bonnet, I found a brown sludge-like substance on and around the oil filler cap. Could this be linked to the HG? I am unsure since a lot of other posts seem to link a HG problem to a white mayo-looking substance instead. Also, there are no signs of contamination on the dipstick, and there is no evidence of a loss of coolant.

Any suggestions?

have you been doing a few short trips, apparently that can cause condensation in the oil and lead to the funny looking stuff in the filler cap, don't think it's anything to worry about if you're not showing HG symptoms and coolant is obviously not contaminating the oil

Yes all I have done lately is short trips. Would you suggest a good long drive of it just to be sure? I'm thinking that a long trip would get the oil up to a higher temperature so wouldn't condense??

Yes. But only way to be 100% is to do a compression test. Compression testers are about 15 quid posted on eBay. They're not the nicest, but they'll do the job.