The challenger bank boss said not giving customers the opportunity for face to face interaction is taking away choice.
Metro Bank has 48 branches at present, but Donaldson said its target is 250 or maybe 300 across the country.
It comes as HSBC is the latest big bank to close branches and cut jobs, saying 90 per cent of its interaction with customers now takes place via digital. The high street bank will close 62 branches bringing its total footprint to 625 in the UK by the end of the year.
"There's definitely space and opportunities" for the crop of digital-only challengers such as Monzo and Tandem, said Donaldson, speaking at The Economist's Finance Disrupted conference in London on Wednesday.
However, partnering with a bank such as RBS to let customers of one unnamed digital bank cash cheques and delivering cards by post demonstrates their limits.
"That's not digital," said Donaldson.