It's very hard to get this kinda longer-term therapy for free. As I'm sure you may have guessed or experienced, NHS waiting lists can be very long!
Since you're at uni: if you have any mental health official diagnoses, your better bet (if you're not in the final year of your degree) might be to apply for Disabled Students' Allowance if eligible. If it's approved for you, you might be offered weekly sessions with a specialist mental health mentor. They would not be your therapist or your counsellor, but they might have backgrounds in those areas or related work. It would be a regular point of contact throughout your degree, at the very least
How? I'm located in Leeds, under 25, no money. Need to talk about multiple issues- body dysmorphic disorder, growing up as a 2nd gen immigrant, low self esteem, self harm, social anxiety.
Your best bet is to get a referral for talking therapies through your GP. You will have an assessment with a practitioner and referred to the most appropriate service. You may be offered shorter term low-intensity therapy first if you haven't had therapy before, or you might be directly stepped up for high-intensity support, which is more medium-term support. At step 3 (high intensity services) they can usually offer up to about 20 sessions (maybe more in some cases). Waiting times for these services are quite long, but it won't cost you anything.