I agree with others here that the employer won't give you a contract saying "we'll never cancel this contract" (and if they gave you one saying "no party will ever cancel this contract" you may have a problem). In addition, I have a suspicion that the employer agreeing to not cancel the contract is maybe not what you actually need: what if it's not your prospective employer who cancels the contract but their government decides to not let you in (not even with quarantine)?
So instead, find out what the actual, precise practical problems are, and then think about solutions - first yourself, then together with your prospective employer:
- their economic situation? Not much you can do about this - but they presumably know what they are doing, and the situation is not that new any more for them. You did your homework about the employer's reputation, did you?
- your financial risk of eating the cost of plane tickets etc.? There are ways to greatly mitigate those risks: e.g. a combination of travel insurance and flexibility about the start date can go a long way here.
So IMHO it does make a whole lot of sense to talk to the prospective employer how various situations will be handled.
If they reimburse you for the relocation, either have them book your flights or have them explicitly tell you what you should do in terms of travel insurance, how long in advance you're supposed to book etc..
If all the costs of the relocation are up to you, consider whether the internship is worth while for you if those costs go up significantly, e.g. you have to quarantine at home and while the travel insurance you took out reimburses you for the unused ticket, booking the next flight when you get released from quarantine* will likely be more expensive. If the internship is not worth while under the risk of such elevated relocation costs, politely cancel your application now.
If you think it unlikely but not impossible, talk to them how such a situation will be handled:
I think you may ask them how flexible they are in terms of your start date with the example scenario of you needing to quarantine before leaving (could you go for the cheaper flight "in 4 days" instead of the very expensive one "tomorrow" when you get out of quarantine).
You may consider booking your flight so that you can do a 2 week quarantine in the UK. In case that quarantine is not required, could you start work 2 weeks early? Or would they prefer you starting 2 weeks later in case you have to quarantine even though that is not a requirement now when you book the flight?
Do you have your visum already? If not, take care of this asap. Having the visum will mean one uncertainty less.
* You may not rely too much on being released from quarantine after exactly 2 weeks. E.g. if meanwhile a new member of your household develops symptoms, the quarantine clock may be reset, and/or release from quarantine may also be bound to negative PCR tests after the quarantine period.