Logically that would seem to be okay, since a UKARA registration's function is to ensure that a retailer is selling a RIF to someone who is using it for airsofting, and that is ultimately what you would be doing, but in regards to granting registrations, the UKARA site does actually state that 'to become UKARA registered airsoft player you are required to take part in three games'. So unless you get your parents to do that, then technically it's outside of the requirements for a registration.
Having said that, I would ask at the site itself. I'm pretty sure they'd tell you the same thing I have, but if you don't ask then you can't know for sure if they'd say it was a no-no. However, consider this...
It isn't actually a legal requirement for someone buying a RIF to have a UKARA registration at all, since all a UKARA registration is, is a convenient way for a retailer to check if the RIF which they sell is going to be used for one of the legitimate purposes listed in the VCR Act (i.e. for airsoft games). The UKARA scheme is not mentioned at all in the text of the VCR Act and is in no way a 'license', although it is mentioned in the VCR Act's guidelines. So if a retailer can be absolutely sure that a RIF which they sell is going to be used in that way, then it is not illegal for them to supply it. An example of where that would be entirely legitimate, is if you were a regular at a site which had a shop, and your parent came in with you and said they wanted to buy a RIF for you as a present. The shop staff could be certain that it was a legitimate sale because they would have seen you regularly skirmishing and would therefore know that the RIF was going to be used for a legitimate purpose, and in fact that would actually be a bit more sound in terms of legality than checking a UKARA number, since how can a retailer really know that someone has not simply gone to three skirmishes, got registered, bought a RIF, and then never gone skirmishing again, nor has any intention of ever doing so again?
What would not be okay, is if you gave a parent the money so that they could buy it for you, since it has to be a gift, but of course who would know if that had occurred?