UK Smart Meters don't need broadband or Wi-Fi. These use their own mobile or proprietary system depending what part of the country you are in.
So go ahead and get a Smart Meter, you shouldn't have any problems, and you won't need to change your current set-up.
You can't refuse a Smart Meter if yours is faulty or out of certification.
See a good list of pros and cons on this website: https://www.smartme.co.uk/good-or-bad.html.
Overall I'd say get a Smart Meter - even if it doesn't communicate it's no worse than a traditional meter.
If your meter is out of certification your supplier must try to fit a smart meter unless there is a technical reason why they can't. They do not need you permission.
See Traditional Meter Certification Expiry on this page https://www.smartme.co.uk/roll-out.html. This rule is called the "New and...
The information from the gas meter gets sent every half hour, so there is a delay. This is to maximise the life of the battery in the gas meter.
How often will my IHD be updated with data from my meters?
Your IHD (In Home Display) will be updated by your electricity meter about every 10 seconds...