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did you not receive a HH5. BT do not get openreach to issue modems now that HH5 is modem/router
Even if there isn't, there is administrative work to do that has to be paid for.
In order to activate your BT Infinity service, an engineer will need to visit your street cabinet and in some cases carry out work in your home – all for a small, one-off activation charge of £49.
Can't see where you have any grounds for complaint.