At what university? For nationwide comparisons, I'm pretty sure only UCAS have the relevant data and I'm not sure they publish such things, so anything else is speculation...
For an individual datum, Cambridge does publish data
on success rate for applications to their courses. In 2017, undergraduate entry Medicine at Cambridge had a success rate of 19.2%, slightly below the average across the university of 20.3%. Architecture was the most competitive standard entry course, with just 8.6% success rate, although graduate entry Medicine was the most competitive overall at 5.8% of applications being successful. In total there were 10 subjects (including graduate entry Medicine) at Cambridge which had lower success rates, which included all STEM subjects except Natural Sciences, Veterinary Medicine, and Psychology & Behavioural Sciences, and five "arts" subjects (Philosophy, Economics, HSPS, Law, and Architecture). However, Medicine at Cambridge has considerably fewer applications per place than other medical schools due to self selection of applicants.
By comparison, in 2016 Economics with Economic History at LSE had 63 applicants for a single place, with only a 1.6% success rate. Econometrics and Mathematical Economics at the same university/year had 163 applications, of which none were accepted. The most competitive course otherwise at LSE in the year indicated was Politics & International Relations, with a success rate of 4.4%. However, LSE also not infrequently makes offers for other courses (e.g. other joint honours combinations) to unsuccessful applicants, so the candidates may have been successful in getting a place on their first choice of course may still get a place on another at the same university, which may or may not be in or related to their desired subject area.
It's unlikely there is any non-trivial answer to the question, if for no other reason than because I doubt there is any one degree subject offered by every university which would allow anyone to reasonably compare competition ratios and success rates at. In fact I don't even think there is any one subject offered by all of the Russell Group alone; Maths I think is the only one if you count joint honours courses. Additionally an individual subject may be competitive at one/a few universities, and largely uncompetitive elsewhere (e.g. many Economics/Business/Finance courses which are likely to be more competitive at a few "top" universities and less competitive at universities that are not "target universities" for investment banks, which is a goal of many students applying to such courses; similarly Law). As a result, there would be a much wider range of competition ratios for those subjects and so the average gets skewed as a result, despite those subjects potentially existing in something of a two-tier system.