Walking away without paying comes under three possible criminal acts:
- The Theft Act 1968: defines crimes related to "dishonestly appropriating property belonging to another with intention to permanently deprive the other of it’". ("Appropriating" basically means treating the objects as if one was the owner, so taking it to keep or to sell, etc). This is the basic definition of theft in English law.
- The Theft Act 1978: defines the crime of making off without payment
- The Fraud Act 2006: defines crimes related to obtaining goods and services dishonestly by deception, or creating gains and losses (for oneself or other people) by dishonest false statements, etc.
In your case, there is initially no dishonesty. The person visited and ate, and clearly intended to pay. After eating, they queued up and waited to pay.
If they do not at any time act dishonestly (by giving a false address or details, or something else dishonest), then they cannot be guilty of an offence under either the Theft Act 1968 or the Fraud Act 2006, full stop.
(Note that the law is quite exacting here. For example, even if they impulsively decided after eating, to dishonestly evade payment, because of the payment issues, technically the meal and services they already enjoyed, were not obtained by any dishonesty or deception, or with any intent to evade payment!)
That leaves the Theft Act 1978. Section 3 defines the offence of "Making off without payment". Cutting out irrelevant clauses, it says that the offence involves "a person who, knowing that payment on the spot for any goods supplied or service done is required or expected from him, dishonestly makes off without having paid as required or expected and with intent to avoid payment of the amount due".
That means, it is only a crime if (1) done in a dishonest manner, and (2) the aim was to avoid payment.
So for example, leaving your correct details, or even leaving no details but being able to persuade a court that you did intend to return and pay the amount, or even disputing the amount in an honest manner but giving them enough details to sue you ("I don't think you deserve payment because of the delay, but sue me if you disagree. Here is my address"), would all be enough to stop it being a crime.
Wikipedia confirms that this was the way the courts see it, as well: "In R v Allen, the House of Lords said that, in order for the offence to be committed, there must be "an intention to permanently deprive" by making off, and that a mere "intention to defer" payment is not sufficient. In theory, a person could eat a meal at a restaurant, not pay, but leave his name and address in order for the restaurant to start civil recovery procedures against him - as long as the details were correct, and he did intend to pay at some point in the future (by way of civil recovery) then no offence under Section 3 would be committed."
As for forcing you to stay, in English law a private citizen can only detain another person against their will, in very limited circumstances. Of which this wouldn't be one, unless they had "reasonable grounds" to believe a crime was being/had been committed, and the action was necessary. This moves into the area of citizens arrest, right to apprehend, false imprisonment, (un)lawful detention, assault (physical contact), affray and other similar crimes (causing fear of harm in another). They would be at great risk of those, and would have to prove they were not culpable, and you would have the right to resist or use reasonable force if needed, to escape them, if you acted honestly, had an honest belief they were acting unlawfully, or your response was "reasonable". But it's hard to cover that aspect in depth because it's so deeply tied into exactly who did what, and who believed what, and on what basis, and how reasonably.