It’s not really a ‘thing’ in the UK. Our banks don’t use coin rolls… they use small plastic bags. Searching those bags isn’t particularly fruitful because we switched to decimal coinage in 1971, and that’s the earliest dated coin you’re going to find. Even then, only the 1p, 2p and 20p coins have remained unchanged in size with continued circulation. Both 5p and 10p coins were released in large numbers from 1968 onwards and 50p coins from 1969 onwards to familiarise the public with the impending switch, but have since been replaced with smaller versions. The 1/2p was withdrawn in 1984, the 5p was replaced by a smaller version in 1990; the 10p by a smaller version in 1992; the 50p by a smaller version in 1997; and the round £1 by a 12-sided version in 2017. The £2 only appeared in 1998, including a delayed stockpile of coins dated 1997. All pre-decimal coinage has been withdrawn.
There are no silver coins to be had (apart from very occasional silver proofs/commemoratives inadvertently being put into circulation by members of the public), no rare dates per se, and no mintmark variations to be found since we only have one mint producing coinage.
There are a number of subtle die variations and combinations of interest to collectors, none of which have particular value, but only a handful of major mint errors with unintended die pairings worth looking out for, plus the usual assortment of striking flaws and other errors.
Really, the only coins in current circulation likely to have significant value are in the 50p series, which includes a number of commemorative and novelty reverse designs, some of which had very limited mintages.
It’s pretty much the same for most other European countries. Out of 27 EU member states, 20 of them have switched to the euro as currency since 1999 and older coins are no longer in circulation.