However, as their press release notes:
Westminster Bridge, one of London's most iconic landmarks, lies between the Houses of Parliament on the north of the river and St. Thomas' Hospital on the south. UK Uncut claims that "by blocking Westminster Bridge, we symbolically block the bill from getting from Parliament to our hospitals". In a message to supporters entitled "Block the Bridge, Block the Bill", the group encourages participants to adopt tactics including lying in pools of fake blood, performing pretend operations and having picnics overlooking Parliament.
There is an issue with this.
St. Thomas' is the main hospital for the City of Westminster, the bridge is the normal access point. With a blocking of the bridge and possibly a police presence around the area to deal with the protest access to St. Thomas' Hospital is liable to be restricted. Therefore forcing emergency services to have to try and get to Guys or St. Barts. This could lead to a delay in these emergency services .
Some of the above would apply on a normal day. October 9th isn't a normal day. The Bridge will already be closed off as part of the Royal Parks Half Marathon route. So ironically UK Uncut will be blocking off an already blocked off bridge but on top of that will be causing disruptions around an NHS facility possibly causing it to refuse to take emergency cases.