The rule has already been place in London for more than 40 years but Department for Transport (DfT) officials are hoping to expand it across the country including into Yorkshire.
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The proposal has been suggested by DfT previously with drivers potentially hit with £70 fines for mounting the kerb but were never introduced.
However, according to the Metro, the government is now once again looking at the issue as part of a wider overhaul of traffic regulations.
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“However, the department is now undertaking a broader piece of work to gather evidence on the issue of pavement parking. We expect to be able to draw conclusions later this year."
A Sheffield council spokesperson said: "Highway authorities already have some powers to prohibit parking on pavements, and we would be interested in any proposals that would help to address these further, especially if they allow greater flexibility and discretion to be applied by civil enforcement officers while ensuring a consistent approach to motorists."
A bill allowing councils to ban pavement parking over wide areas was debated in parliament in 2015 but it was withdrawn without being approved.