The option to "stay on existing plan" only means you can stay on it until 1st September, when most existing plans are being discontinued, and being replaced by the new Unlimited Minutes, or else you can opt for 700 Minutes or PAYG.
From what I've read, the figure of £4.50 extra is very misleading - apparently it's based on BT's estimate that most customers currently pay at least £10.50 per month on calls.
The new Unlimited Minutes plan costs £15 per month per BT's Consumer Price Guide leaflet. If you have been in the habit of using £10.50 worth of calls, then yes, the new plan will cost you £4.50 extra.
From MSE: "BT says affected customers pay at least £10.50/mth at the moment, so the maximum price hike will be £4.50/mth – or £54/yr. However, it says for many the price increase will be less, and after factoring in what customers currently typically pay on out-of-allowance calls, it estimates the average net price rise will be £1.83/mth."
If you normally pay, say, £12 on calls, the price rise will only be £3 extra.
But if you normally spend, say, £3 per month on calls, the new plan will presumably cost you £12 extra, and so on.
For years I've had Unlimited Anytime bundled in with my broadband package, so haven't paid anything extra for calls unless I've called a service number, or have gone over the 60-minute limit for any one call (though I dare say an amount for calls has been included in the package cost). This means I've only spent £2.08 on calls outwith the plan in the last year.
The new plan will therefore (I assume) cost me about £178 extra per year, or over £14 extra per month.
Still trying to get through to BT , but so far, if the above is indeed the case, it looks as if PAYG will be cheaper for me.
** On the other hand, on looking at page 25 of the BT Consumer Price Guide leaflet:
https://www.bt.com/assets/pdf/BT_PhoneTariff_Residential.pdf
it says, re the figure of £15, " This is a maximum price; some customers may pay less". What on earth does that mean??
