"The EU has not and would not force us to use the euro. End of."
If would if we remain in the EU.
The UK (along with Denmark) opted out of adopting the euro upon its launch in 1999 as an accounting currency (followed in 2002 by the issue of banknotes and coins). Sweden joined the EU in 1994 and as such was obliged by the Treaty it signed to adopt the euro. However they held a referendum in 2003 which resulted in a vote against adopting the euro. So they too are out - for the time being.
Apart from the UK and Denmark, all other EU nations currently using their own currencies are obligated to adopt the euro as soon as they meet the convergence criteria. (As an aside, those criteria are extremely flexible. At least two current euro nations - Greece and Portugal - failed to meet them by a country mile). Any new members face a similar obligation. There is little doubt that with the EU’s quest for “ever closer union” together with its plans for fiscal intervention in sovereign nations’ affairs (which it has already demonstrated in Greece) that it is unlikely to tolerate one or two rogue nations controlling its own currency exchange and interest rates. It simply does not suit their plans.
When discussing the referendum result it is often said that those who did not vote failed to do so because they were happy with the “status quo”. Well I have news for them – there is no “status quo” as far as the EU is concerned. It has spent more than 40 years nibbling away, salami style, at national sovereignty with the sole aim of creating a single nation called Europe. That process is ongoing. Of course a nation cannot realistically have a number of different currencies in use in different parts of its area - especially when the expected fiscal integration has become more profound. So there is no doubt that Denmark (and the UK had it remained) will be whipped into line as soon as circumstances permit and the control they have over their currencies and interest rates will be swept aside.