Should I be worried about this tropical mosquito in east London?

It's not really being blown out of proportion - these mosquitoes (Asian tiger mosquitoes, I'd guess) can carry dengue and other diseases, which is a legitimate concern. That said, established breeding populations in the UK are still pretty rare, so while it's worth being aware and reporting any you spot, the actual risk to most people remains quite low for now.

The concern is real but the actual risk to you personally is still pretty low right now. These mosquitoes do carry diseases like dengue, but they need an established population to become a genuine threat, and that takes time. What matters more is whether you're in an area where they're actively breeding - if you are, just use standard precautions like keeping standing water out of your garden and using repellent when you're outside during dawn and dusk when they're most active. The bigger picture is that public health officials are monitoring this specifically because catching it early stops it from becoming another seasonal nuisance like we've seen in other parts of Europe, so the attention is actually doing its job.

The main thing is to keep your gutters and outdoor containers clear of standing water - that's where they breed, and it's something you can actually control. The disease risk gets overstated a bit in the news. Yes, tiger mosquitoes can carry dengue, but they're not that established in London yet, and you'd need to be bitten by an infected one, which is still quite rare here. The real concern is if they do establish proper populations over the next few years, but for now the precautions are just common sense: empty plant pots, bird baths, drains. Keep an eye out for the distinctive striped legs if you see mosquitoes around, but don't lose sleep over it.