It is hard to get away to compete in sport whilst in Basic training, however I did get pulled out of Basic training to run in the Army Championships 800m back in 1988 against the wishes of my Platoon Sgt so it can happen in some sports if at a good level. Its a bit difference with the training for boxing to running so extremely unlikely and as said training staff are not happy that your missing vital military lessons. As Falls says though once in Bn then lots of scope and plenty of boxing comps in Colly.
If you get accepted for training, you will not have time to visit any boxing clubs, as you will be too busy with military training, exercises, etc. But once completed, you are free to try for your unit's boxing team. This will include full-time training, in the run up to the inter company championships.
Some units have a pool of guys on full time training most of the year round.
On P Company, there is a Milling event, with two men facing off in a makeshift ring made of four benches and some mats on the floor, with the rest of the lads sat on the benches, and putting their arms up to stop any fighter leaving or falling our of the ring. You fight for a full minute, fists flying, no blocking, bobbing and weaving. The staff want to see a good solid toe to toe scrap. Win or lose is not important. It is more important that you give your all.