I don't think the headline is strictly true.
The EMA are saying one thing but national states are saying another in terms of what it means for British Citizens and are prepared to just count it as AZ rather than Covishield. (It sounds like Austria, Germany, Slovenia, Greece, Iceland, Ireland, Spain and Switzerland at least are fine with it).
The EMA don't actually have legal power to bar Brits and thats the significant part.
The other thing is that it depends on how the UK certify Brits. By the sound of it, they are recording all AZ vaccinated Brits under the Vaxzevria AstraZeneca brand so that you can't tell the difference between who has had the EMA approved EU manufactured vaccine and the Indian manufactured vaccine. Its unlikely to mention batch so no one at the border will be able to tell.
I think the situation with the US is more difficult as AZ isn't approved there and its apparent that talks to open a travel corridor with the US are stalling because the CDC hasn't approved AZ (or Covishield).
The UK has some more leverage here I suspect because I think this potentially would fall under the remit of the ECHR and there would be arguments on the basis of discrimination. Its worth noting that those who got the Indian batches will have been vaccinated in March / very early April so will be mainly those in their 50s. Thats going to include people who may need to travel for work too.
The key stumbling block is once you've had one vaccination, you can't exactly go back and take another one just to pass immigration.
So at some point there is going to have to be proper international cooperation on this - particularly with countries that have close links to each other.
I'm not particularly worried (I'm actually one of those affected). Its just needs so heads banging together on the paperwork.
Lets be honest, why on earth would tourist destinations that rely on British visitors want to stop fully vaccinated Brits (and importantly EU citizens resident in the UK) from coming just because they have the wrong batch number?
The MRHA is still highly respected and checked these batches coming in to British standards. Whilst we aren't in the EU, EU countries aren't out of their minds either - and not recognising Brits as fully vaccinated on the basis of batch numbers makes no sense to anyone whatsoever.