It is a good thing that vaccines are looked at carefully, paused and evaluated for concerns, it is the mechanism for them being safe in the long run. Canada, and Norway are not in the EU and they have concerns. The US flagged inaccurate efficacy data and it was resolved. This is a good thing.
The US is a separate issue, they've not approved AZ yet. I have no issue with that, the FDA have an excellent record and have slightly different requirements than the MHRA or EMA (as long as I've worked in the industry there have been attempts to align the US and EU requìrements for approvals but we're still not there). This is completely normal.
However, the EMA have at no stage suggested the putative side effects that have been reported for AZ are serious enough to recall the vaccine, the usual response in this situation would be to review the evidence while still using the product, this is what the MHRA have done and what the EMA have recommended be the EU response. Countries pausing their vaccination programmes are acting politically, not scientifically. This may be for internal reasons (e.g. Franch has a large anti-vax population that need to be appeased) or for Brexit reasons. Who knows?
I've got my vaccine next week, don't yet know what I'll get but I assume it will be AZ and I'll take whatever I've given. There have been enough people vaccinated that we know the vaccine is less risky than Covid, even if the concerns turn out to be valid the incidence is very rare. The vaccine won't be withdrawn, but there may be different advice on the product insert.