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That modem is badly obsolete, and there's a good chance that they will get a faster and more stable connection with a more modern router, so it probably makes sense to upgrade regardless of the technical problem.
I'd be inclined to switch broadband providers, because they'll get a free router and will probably get a better deal. There are currently some excellent deals available, often including cashback - if you sign up for Sky Broadband this week, you'll get a free £100 M&S voucher after 90 days.