COVID-19 Outbreak Information Updates (Reboot) [over 150.000,000 US cases (est.), 6,422,520 US hospitilizations, 1,148,691 US deaths.]

Could also be that Omicron hit just on the backside of a mass booster effort in UK while the US was caught months past the time we had a big booster push and immunity waned that it makes the efficacy appear a lot lower.

I'm laying big money on the ability of vaccines to prevent infection being a lot lower in the US. I'm also betting that timing boosters with waves becoming a big part of the battle against covid. It's really no different than what we do with flu vaccines because it is making little sense to push boosters at times that efficacy becomes reduced when needed.
I don't think there was much difference in initial timing between the booster effort in the UK and the US. The UK started late September, and that was also when the US's booster dose recommendation was given according to the CDC data tracker (https://covid.cdc.gov/covid-data-tracker/#vaccination-trends). The US had been boosting before that, but at a relatively low rate, <100k per day.

The difference, I think, is in scale. In October, the UK was boosting around 200-300K per day, rising to around 350k per day (~0.5%) of the population through November. (https://coronavirus.data.gov.uk/details/vaccinations). The US was boosting around 400k per day in October, rising to 900k per day in November. But that's still only around half the rate per capita in November for the US compared to the UK.

So prior to Omicron showing up and really kicking in, both countries had started pushing boosters, but the UK had actually been boosting substantially more relative to population than the US already.

And then after Omicron had started making noise, in December, the UK had an additional push which took the levels substantially higher still, up to nearly 900k per day (~1.3% per day). The US only had a small increase over November levels (with a dip over Thanksgiving as well).

So both countries really started pushing boosters around the same time, but the UK has been boosting at a higher rate right from the start of official recommendations in late September, and had an additional really big push in December. The US has just been consistently boosting at a lower rate. At this point the UK has given out over 36 million booster or third doses, which represents 62.9% of over 12 year olds. In the US, it's over 78 million, but that's only 40.6% of over 18 year olds (UK dashboard is giving those percentages in terms of over 12 year olds, and I'm not trying to convert that right now, but you can see it's a substantial difference even without that).

So while it's true to say a higher proportion of boosters in the US were given in the earlier part of the period compared to the UK, that's not because of an earlier big push in the US; rates have risen as time has gone on, they just haven't risen that much, relative to the UK. With the UK consistently boosting at a higher rate, I'd suggest the more significant difference is likely to be the relative absence of boosters, rather than the relative timing.

I have seen some discussion about timing boosters with waves, but I think the problem is in predicting them. So far, Covid hasn't as seasonal as flu, for example.