Having a separate bank account for your business expenses and income keeps your business spending separate from your personal spending and enables you to easily see if your business spending is exceeding your business income. Business expenses must be wholly and exclusively for the purpose of running the business so if you are using your business bank account as another bank account for personal spending you will still never be able to keep track of how your business is doing.
Limited companies must have a separate bank account because a limited company is not an extension of you as it is if you are a sole trader. A limited company is a separate entity to you and its income and expenses must be kept separate.
If you are a sole trader muddling up your business spending with your personal spending creates a lot more work when you need to identify your business income and business expenses in order to produce figures for your accountant or to prepare your tax return. If you are using a bookkeeper or an accountant to do your accounts why would you want to pay them to separate out your business and personal spending.
The best thing you can do when you start trading is to have a separate bank account which you use to receive business income and pay for business expenses from. If you don't have enough money to pay for everything you need to buy you can transfer personal money into your business bank account and, when you have sufficient funds, withdraw some or all of it. This would be classed as a temporary loan from you to your business which is not regarded as income, nor as an expense when you repay it.
However if you take money out of your business for personal use - whether it is paying for some shopping, buying some "work" clothing which isn't actually allowable work clothing, or buying yourself lunch - this will be recorded as a personal expense within your accounts and will not be tax deductible. And if you cannot provide receipts for purchases which may or may not be business they will be recorded as personal as there is no evidence to prove they are a business expense. If you only ever use your business account for business spending there will never be a question over whether the purchase is business or personal; the only question that will remain is whether it is an allowable business expense for tax purposes.
Paying yourself a regular amount from your business account to your personal bank account for your personal spending will ensure your accounts are more easily maintained and reconciled and will keep the costs down if you choose to ask a bookkeeper or an accountant to do your books. And when HMRC visit to do a records check you will only need to give them access to your business bank account records rather than all your personal spending too.
So the answer is definitely a Yes to a separate business bank account. Keep your personal spending separate. And of course, any business expenses which you have paid from your own pocket can be recorded in your accounts and reimbursed to you tax-free.