The Health and Safety Executive (HSE) said five rides were re-inspected and temporarily taken out of use after the incident at Ohio State Fair on July 26.
A sixth ride at Lightwater Valley in North Yorkshire was immediately taken out of use by the operator independently of the HSE.
Tyler Jarrell, an 18-year-old high school student, died when a swinging and spinning ride called the Fire Ball broke apart. Seven other people were injured, some critically.
Three of the closed rides are at Pleasurewood Hills theme park in Suffolk, Coney Beach Fair in Porthcawl, South Wales, and Brean Theme Park in Somerset, the HSE said.
A fourth is operated by Ryan Crow Amusements at funfairs in the North East, and a ride owned by a Joseph Manning in Hertfordshire has also been served with a prohibition enforcement notice.
Lightwater Valley said its Eagle’s Claw ride was not running, telling visitors: “Due to circumstances beyond our control this ride is currently closed, apologies for any inconvenience this may cause.”
The HSE said it was aware of the “tragic accident” involving the KMG Afterburner, which was themed as Fire Ball in Columbus, Ohio.
A spokeswoman said: “There are six machines of this version operating in the UK which were all thoroughly inspected within the last 12 months in line with agreed procedures.
“There is no verified information regarding the immediate cause of the US accident. Following the incident, HSE initiated a re-inspection of these machines.
“As a result, on Friday 28 July an enforcement notice was served on five of the machines, which are now to be taken out of use until the notices have been complied with.
“The sixth, at Lightwater Valley in North Yorkshire, was immediately taken out of use following the incident in Ohio.
“This was a decision taken independently by the operator. Lightwater Valley has agreed to keep this machine out of use until the other five notices have been complied with.”
The HSE said it understood a letter had been sent to operators of all similar machines operating in the UK and that some owners may have closed rides “as a precautionary measure”.
It added: “HSE will ensure operators are kept abreast of information as it arrives and will take such action as is necessary to ensure the rides are inspected and tested as necessary to ensure safety.”
Manning’s Amusements said: “The safety of our customers is, of course, of paramount importance to us. We confirm that, as a precaution, the Afterburner ride that was being operated by us was immediately taken out of service pending a full investigation being carried out.
“We are liaising with the HSE and the ride will not re-open until all tests have been completed and we are fully satisfied that there is no risk to passengers.”
A spokesman for Lightwater Valley said the theme park was “deeply saddened” to hear of the US incident.
He continued: “While there are fundamental and significant differences between our ride and the one involved in this terrible incident, we entirely support the HSE’s decision to not operate these types of ride in Great Britain until all the facts are known and a comprehensive investigation has taken place.
“Our ride has undergone the most stringent of safety checks, however as a precaution we strongly believe this is the correct and responsible thing to do. The safety and wellbeing of our visitors is of paramount importance.
“We will, of course, notify the public when the ride is back in operation.”