TL&DR It seems that your only option is to obtain an Amateur Radio license for all those who need to use the Baoffeng hand sets. The sets do not qualify, or is unlikely to qualify, for any license exempts nor for business radio use.
Disclaimer: I am not a lawyer, and although I am quoting legislation, for legal advice please seek advice from a lawyer in your country.
My Question being is it legal for me to use these radios without a
No, is the answer.
Sorry to "bust the bubble" but unless you get an Amateur Radio license you may not use these sets.
You may NOT use them on PMR/446-MHz, as they are not typed approved. Legislation here
2. Prescribed apparatus taken into service before 1st May 2000 must also—
(a)be approved by the Secretary of State under section 84 of the 1984 Act for the purposes of these Regulations; or
(b)be approved to the standard referred to in Part IV of this Schedule by a national administration following type testing at a test laboratory
The correct answer (already given, and I can only repeat this) is to get an Amateur Radio license for all those who want to participate.
would it be possible for me to obtain a Simple Business licence within
the UK without being a registered company?
I believe you can get a Simple Business license, you just need to apply. If you can use the Baoffengs?... that need to be seen, but my best guess here is: No, as the legislation is hinting to being licensed to particular equipment, or equipment with specific specifications (which I am doubtful the Baoffeng would be classified):
Requirements that must be met for the grant of a licence
5.—(1) Licences shall be granted by OFCOM, either—
(a) in relation to particular equipment; or
(b) in relation to any equipment falling within the description specified in the licence and expressed by reference to such factors (including factors confined to the manner in which it is established, installed or used), as are described in the licence.