Different A&E departments have different problems. The NHS is the largest employer in Europe, and it's reductive to say "all London hospitals are understaffed". They are not. Part of the problem is seasonal and even daily shifts in A&E visits, you can't staff for the worst case all the time. And January/Feb is known to be a busy couple of months.
I recently moved to a new state and I’m trying to get set up with a new primary care provider. I’ve been trying to get an appointment for six months, but they keep bumping my appointment back. Did I mention that I had to settle for a nurse because none of the doctors in my area are accepting new patients?
That is because NHS spending is being slashed viciously. Obviously, if socialised medicine is being dismantled, it can't be expected to work all that well anymore.
My experience was very different. In January-February this year I had to visit (unfortunately) both the Emergency Room in NYC and the A&E in London. While the quality of the medical equipment in London matches the one in NYC, the understaffing is much more severe. In neither place was my wait time only 10 minutes, but in NYC I had to wait for about 1 hour (including paperwork), while in London for about 6 hours.
I talked with other people in London about my experience that the medical system is severely understaffed, and all agreed. On the plus side, I did not have to pay anything in the UK (they didn't even care that I was not a UK resident). In the US I had to pay north of $1000, despite having insurance.