Vodafone offers a basic PAYG Sim which doesn't require a credit check. But it no longer offers 'traditional' PAYG (where a customer tops up using credit and uses that for calls, texts and data). Instead, it offers data packs which start from £10/month and last for 30 days.
The cheapest Vodafone Sim costs £5.59/month and it currently offers unlimited minutes & texts and 4GB/month data - though it's on Vodafone's Basics' plan, which means you can't use it abroad. See cheap Vodafone Sims.
Yes, you can keep your old mobile phone number. If you're moving from another network, you'll need to text 'PAC' for free to 65075 to request your PAC (porting authorisation code). You will need to provide this to Vodafone which should move your number over within one working day.
If you are already a Vodafone customer, you'll need to fill in a 'keep my number' form on its website.
If you signed up to Vodafone before 11 August 2021, depending on your plan, you'll be able to roam in up to 81 countries without extra charges. If you signed up after this date, you'll be charged £2/day if you wish to use your allowance within the EU. To use your allowance in a country not included in your plan, you can purchase one of its Roam Further add-ons, which cost £6/day. For more info, see Cheap Roaming.
Yes, Vodafone offers 5G on most of its Sims, but not its 'Basics' Sim. However, be aware you'll need a 5G-compatible phone too.