Research your constabulary. They should have a careers page where they discuss the requirements for the role. It is steadily changing, however, and policing is being treated as a "professionals" job, much like paramedics and doctors. Therefore, some sort of relevant qualification may now be required, but they should give you this information (if they don't, contact them and ask about the future requirements - It is better to be prepared early than un-prepared too late). Requirements may include (it really depends on the constabulary):
1) A CKP (Certificate in Knowledge of Policing). It's a ~80 hour course taught at some colleges and universities with assessments along the way. Be sure it is an accredited course or else it is worthless to the police. The CKP may be phased out in the future, but it gives you an overview of the basic laws and procedures required.
2) A policing foundation year (1 year), or foundation degree (2 years) or a degree (3) years. They may accept things like criminology, but anticipate that they'll want you to go on a specified course and they may not accept anything else. In some cases, you may be expected to be a serving Special Constable or be eligible (and then become one on the course) in order to join their policing degree. Some constabularies have partnered with a sole university whom, and whom alone, provide the course as a pre-requisite to joining.
3) A degree in any subject. This is more towards the fast-track schemes where they want candidates with a 2:1 in pretty much any degree. If accepted (and places are minimal), you'll do 3 years of service and become an Inspector at the end of it.
4) You may have to be a Special Constable in order to apply to some constabularies. I thought that was the policy with the Met but it seems to have changed.
5) None of the above. In some cases, you can just rock on up and fill out an application. However, what you might lack in formal education you will have to make up for doubly in life skills. Life skills are important to all candidates, even those with degrees, but you need to show them that you're a capable individual. Going to university, if nothing else, gives you an opportunity to mingle and get involved in circumstances you'd never normally have to deal with. Maturity is always a bonus, but you may already have that.
There are some good things you can do to aid your application or career though. Joining as a Special Constable will allow you to become a fully operational police officer with full powers of arrest. The CKP syllabus includes lots of elements which are taught to Specials, so you can gain knowledge that way. It will also show that you're eligible in terms of medical and security requirements and that you'd be a more capable candidate. Being a Special does not guarantee a Regular position, but heavily weighs in your favour as they'll have much less that they have to teach you. If you've been a Special for a couple of years, you'll know more about the job and know it is right for you - All of these are huge bonuses to them!
Specials are unpaid, work 16+ hours a month (as many as you want to do, and it's usually flexible) and do near enough the same job as the Regulars. There are some specialist elements that you can't be trained to do (or are very rare) such as high-speed driving or becoming a firearms officer, but a lot of the rest is the same.
Doing a degree can help, but it's usually not essential. I think it's worth having a backup plan though. I'm studying engineering and I know it will be easier to do all my university education at a younger age with fewer commitments compared to trying to do it in the future. However, a lot of people will find formal education to be a burden and want to get stuck into their career early on.
In summary, find out what they want and ask them what they expect they'll need in the future. If they run careers seminars, try to get on one and speak to them. If they're at a careers fair somewhere, go and have a chat. The entry requirements have changed a lot in the past 12 months and major changes have occurred on a weekly basis in some cases. I know a few people who have been caught up in that.