There are other factors than dose availability though. Putting vaccines into people isn't easy to do on a large scale in a short time window. Vaccine programmes are usually running with a much larger window, with vaccines that doesn't require extreme cold temperatures.
UK seems better prepared for this than many of the EU-bloc's countries.
The other part of the question however is: "Severely lags behind what?". Even with a "slow" rollout, EU countries in general are better off than many other countries in the world. It isn't the case they are trying to keep up with the pack in general, as they are well positioned. It's more that there are a few countries who are doing extremely well on a quick rollout.