It is comparable to applying for a job to apply for an apprenticeship. In addition to your university applications, you may apply to as many as you like. However, applying for several apprenticeships at the same time is not a good idea.
Remember, there are hundreds of different apprenticeships to choose from. To apply for one, you must first sign up for the Find an Apprenticeship programme. You may also save any apprenticeships that pique your interest and apply for them later.