The advertising watchdog is assessing “a number” of complaints about a Treasury advert stating that duty free shopping will return in the event of a no-deal Brexit.

The Advertising Standards Authority (ASA) tweeted that it was assessing the complaints “carefully against our rules” and advising that there was “no need to lodge any further complaints about this ad”.

An ASA spokeswoman said the complaints were varied but included concerns that the ad was inaccurate and misleading because it implied that a no-deal Brexit would change the fact that people travelling to the EU can currently buy alcohol duty free.

Others complained that the ad promoted tobacco and alcohol, was “Conservative Party propaganda in the guise of impartial government information” or promoted the “illegal act” of a no-deal Brexit.

The complaints to the watchdog come amid wider criticisms that the Treasury’s announcement was “misleading” and “a distraction”.

Under a no-deal Brexit, UK excise duty would no longer be due on alcohol and cigarettes bought when leaving Britain, meaning a bottle of wine bought at Heathrow by a departing passenger would be up to £2.23 cheaper, the Treasury announced on Tuesday.

It said people returning from the EU would have the choice of continuing to purchase and bring home unlimited amounts of cigarettes and alcohol with duty paid – as is the case now – or to buy limited amounts at duty-free shops in EU countries instead.

According to figures provided by the Treasury, someone buying two crates of beer would save £12.

Chancellor Sajid Javid said: “As we prepare to leave the EU, I’m pleased to be able to back British travellers.

“We want people to enjoy their hard-earned holidays and this decision will help holidaymakers’ cash go that little bit further.”

MP Anna Soubry tweeted that the announcement was “propaganda” and “misleading”.

Miles Beale, chief executive of the Wine and Spirit Trade Association, said the announcement was welcome, but added: “It is also a distraction from the main issue – the UK’s punitively high rates of excise duty. Duty free is attractive to UK consumers wholly thanks to excessive and increasing duty levels.

“Wine drinkers in Spain and Italy and 13 other EU countries enjoy duty free purchases without having to leave their shores. The UK alcohol industry is one of the most heavily taxed in Europe, with wine the third highest duty rate – and fastest rising in recent years. And we have the fourth highest duty rate for spirits in the EU.

“There are much bigger issues which would adversely affect our industry in the event of a no-deal Brexit, such as the potential introduction of tariffs on wine.

“So the Government shouldn’t only tinker with duty free allowances for travellers. No ifs, no buts, the Chancellor should go further to back British business and support cash-strapped consumers by cutting duty on wine and on spirits at the next Budget.”

Earlier on Wednesday, Health Secretary Matt Hancock was asked how his vision for health and social care, including England becoming “smoke-free” by 2030, could be squared with “differences in approach” by the Treasury.

At the Public Health England (PHE) conference, Mr Hancock said: “Yeah, I saw that tweet.”

He went on: “Look, I don’t think that the return of duty free was really seen from within a public health context, shall we say, before publication.

“Certainly, I didn’t see it before publication but – leave that one with me.”

In a statement afterwards, Professor John Newton, the PHE’s director of health improvement, said: “Accessibility and affordability makes a huge difference to consumption of tobacco and alcohol and that will remain our advice to Government.”

Elsewhere on social media, the announcement drew concern that it appeared to be at odds with the Government’s aims of cutting drinking and smoking rates.