I assume that you've confirmed that it's taxed via this handy page - https://www.gov.uk/check-vehicle-tax
Sadly it would be very wrong of you to check the insurance status here - https://ownvehicle.askmid.com/
I strongly think that the second shouldn't have the restriction on it.
@MrDrem started
London Fixed Gear and Single-Speed is a community of predominantly fixed gear and single-speed cyclists in and around London, UK.
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I assume that you've confirmed that it's taxed via this handy page - https://www.gov.uk/check-vehicle-tax
Sadly it would be very wrong of you to check the insurance status here - https://ownvehicle.askmid.com/
I strongly think that the second shouldn't have the restriction on it.