Is it reasonable to ask a professor about the strength of a recommendation letter (after they have submitted)?
It would be quite acceptable to ask for a copy of the recommendation letter (although your professor is not forced to supply it). That is probably a more reasonable request than asking if the recommendation is strong, which may require the professor to justify the recommendation.

Once the recommendation is submitted, you would also be entitled to request a copy directly from the institution you've applied to, as this is covered under the Data Protection Act.

Now, as someone who both writes references for students and reads them, I can tell you that the norm in the UK is for them to be restrained and factual. References that are full of hype are generally treated with suspicion.

Academic referees in the UK are also rather limited in what they are allowed to say. There are generally university guidelines which dictate the format. They usually have to be internally signed off before they can be submitted. Then a copy is kept on file.

Choosing referees is something that needs to be done carefully. Even with the best will in the world, an in-demand professor is not likely to be able to give this their full attention.

During my busy periods, when I was writing references for students regularly, I could get up to 20 requests a week. Normally, I'd have to write those in my free time, in the evenings. So, even though I would want to do my best for every student, references for anyone other than students I'd worked very closely with would become necessarily formulaic.

Choosing a referee who has had the opportunity to get to know you, who you have impressed in some way and who is not run off their feet with other activities is generally a sound strategy.