Philip Jansen also held out the possibility that there would be outages and possible security risks if Britain's telcos were ordered to stop doing business with the Chinese firm while the 5G network upgrade was in progress.
British Culture Secretary Oliver Dowden is due to tell Parliament the government's final position on the use of gear from Huawei on Tuesday.
Britain had announced in January that it would allow Huawei to supply up to 35% of gear for the non-core parts of 5G networks.
Following US pressure, applied on Prime Minister Boris Johnson when Washington was approached about a trade deal, Britain agreed to review its earlier stance. New American strictures on Huawei have been taken to mean that any risk mitigation which was possible earlier would not be possible now.
Jansen told the BBC program: “Huawei has been in the telecoms infrastructure for about 20 years and a big supplier to BT and many others in the UK telecoms industry.
“It is all about timing and balance. So if you want to have no Huawei in the whole of the telecoms infrastructure across the whole of the UK, I think that’s impossible to do in under 10 years.”
He said the industry would want to be given a seven-year window to remove Huawei from the 5G network, but said “we could probably do it in five”.
Jansen added that there would be consequences for the UK due to rejecting business with a Chinese company. “At BT and in our discussions with GCHQ, we always take the [view] that security is paramount; it is our No 1 priority," he said.
“But we need to make sure that any change of direction doesn’t lead to more risk in the short term – I think that’s where the detail really matters. If we get in a situation where things need to go very fast, then we go into a situation where service for 24 million BT Group mobile customers is put into question – outages would be possible.
“Secondly, the security and safety in the short term could be put at risk – this is really critical here. If you are not able to buy or transact with Huawei that would mean you wouldn’t be able to get software upgrades if you take it to its specificity.”