You will be able to proceed as anyone with a degree can do the SQE exams - all you need to do is pay the SRA to do the exams.
There are preparation courses available through many providers - most notably University of Law - and they will likely accept you for the preparation course because £ talks. You can do the integrated masters and qualify for the masters loan to cover the costs of the prep course. The cost of the course does not cover the SQE exams.
However, you can self-fund the SQE and prep yourself.
There are 3 factors you should consider if you want to do the SQE and become a solicitor:
1.) The likelihood of you gaining a TC - which will be slimmer than the rest of graduates due to grades
2.) Your academically capability of passing the SQE - The pass rate for SQE is already 51% - and they say this pass rate being too low is from people who aren't academically capable of passing the SQE.
3.) The financial cost of the SQE and preparation course as you can spend nearly £20k and not pass.
However, your grades are going to hold you back and will be an uphill battle in any career route you choose - so you may as well fight that challenge pursing a career you actually want.