Fortunately universities won't be assessing your self-esteem. They'll be looking at whether you're likely to finish the course successfully. And the rigorousness of each institution's assessment will depend on whether the course or university is highly sought after or not.
What was your first degree in? How long is it since you graduated? What have you done since then that demonstrates your suitability for postgraduate study in this particular subject? (Either through work or 'extra-curricular' involvement in, say, Citizens' Advice, volunteering, writing a blog, taking part in research studies, activism ...)
What is your motivation for applying? Personal interest only or are you looking for career progression/ a change in employment?
Have you already identified particular courses? Do you meet their entrance criteria? (These can be quite flexible for mature students.) Have you approached relevant institutions and spoken to the people running the course? (Rather than just to admin staff?)
May seems quite late to be applying for this year. Are you on top of the practical issues? You'll know that if you have a first degree you'll almost certainly be eligible for a Government Postgraduate Loan. (I've been assuming you're considering a concrete university, but perhaps you're thinking of the OU?)
If you pick the right course it can be a glorious experience. (At any age.) But it's also likely to be intense, stressful and exhausting. Thorough preparation is crucial.