What can I do about distressing e-mails or texts?

[canguro]

Do I have any recourse against someone (probably borderline personality disorder) who sends me distressing and unfounded unpleasant e-mails/texts?

Block their number?

Yes, I agree, try blocking their number. There are various apps you could download for free.

If that doesn't work...contact the non-emergency police number.

What has a potential (and it would seem amateur) diagnosis of a PD got to do with anything...?

If it's harassment you can report the matter to police.

Can you provide more details?as

Call 101, they may well take it surprisingly seriously.