Your travel agent will probably have consulted Timatic, which says:
National United Kingdom (GB) /Destination Bangladesh (BD)
Bangladesh (BD)
Passport required.
- Passport and/or passport replacing documents must be valid
on arrival.
Visa Issuance:
Visa required, except for Nationals of United Kingdom can
obtain a visa on arrival at Dhaka (DAC), for a max. stay of 90
days. Fee: Varies per country.
Additional Information:
- Visitors are required to hold proof of sufficient funds to
cover their stay and documents required for their next
destination.
Warning:
- Visitors not holding return/onward tickets could be refused
entry.
It's also very likely that a check-in agent would consult the same source.
Edited to add: also watch out for any transit visa required, depending on the route you take to DAC.
hth