Concealed or otherwise is it legal for a private citizen to carry any kind of weapon for self defence purposes in the UK?
JeffUK has quoted the relevant law. However the question then becomes "what is an 'offensive weapon'", and "what is a lawful excuse?".
Almost anything can be classified as an offensive weapon if you can use it as a weapon. See https://www.askthe.police.uk/content/Q338.htm
A lawful excuse is something like "I am going to play baseball, which is why I have a baseball bat". It is emphatically not "I want it for self defence". Specifically, https://www.cps.gov.uk/legal-guidance/offensive-weapons-knives-bladed-and-pointed-articles cites
Patterson v Block  81 LSG 2458 – carrying a weapon for defence can still amount to intent to cause injury
So the answer to the OP's original question:
Is it legal for a private citizen to carry any kind of weapon for self defence purposes in the UK?
Technically, no, you must have have reasonable excuse or lawful or authority to carry a weapon in public and 'Self Defense' is not normally a reasonable excuse.
However if you mean 'Can I do it without fear of prosecution' then the answer is 'Yes' as long as you can provide a reasonable excuse when asked why you are carrying the weapon.
It's a very nuanced piece of law, the definition of a 'weapon' extends to practically any physical item. It could be both illegal to carry a butter knife, and legal to carry a large machete depending on the circumstances.
Possessing an offensive weapon in a public place is an offence contrary to s 1 of the Prevention of Crime Act 1953.
To satisfy the charge, the prosecution must prove each of the following elements:
- has with him (possession);
- in any public place;
- any offensive weapon.
Having established all of the above, the charge would succeed, unless the accused proves that he had either:
- lawful authority;
- or reasonable excuse.