That also doesn't include many of the newer universities (former polytechnics). There's too many to list, but you'll find dozens of universities which will accept you with any mix of subjects (including BTECs), depending on your grades.
Also, there are a lot of universities which offer Software Engineering degrees (which is a more specialised qualification aimed at learning software engineering skills), so it would be worth investigating those if you're committed to a software engineering career. Again there are dozens of universities which offer this, and it depends a lot on your grades.
Another non-university option could be to apply for a degree-apprenticeship scheme, which involves applying for a job as a trainee/apprentice Software engineer (with an employer who is part of the scheme) and learn those skills on-the-job for 3-4 years (4 days per week) in a professional environment, alongside part-time study (1 day per week) with a university or training provider towards the degree. This pathway is a lot of work and there's a lot of competition for placements (it helps a lot to have a strong programming background before you apply), but it's also a very reliable route into that kind of career if you're already committed to it.