Owners of dogs involved in livestock worrying face the prospect of unlimited fines under a proposed law supported by MPs.

Conservative former environment secretary Therese Coffey has tabled legislation designed to make it easier for police to catch offenders and secure more prosecutions connected to dogs attacking, chasing or causing distress to livestock.

Her Dogs (Protection of Livestock) (Amendment) Bill applies to England and Wales and revives plans paused by the Government last year.

During the Bill’s report stage, MPs agreed to increase the fine that can be imposed on a person convicted of the livestock worrying offence.

Ms Coffey told the Commons: “There’s no limit on that fine, it’s unlimited.”

She said the change would give flexibility to the courts, adding: “I would still expect the Sentencing Council to issue guidelines in order for what would be appropriate.

“But it was deemed important in committee (stage) to make sure that we reinstate that element of making sure there could be an escalation or not some arbitrary cap that Parliament had decided once and for all on what the fine could be, again depending on the severity of the offence.”

Shadow environment secretary Steve Reed offered Labour’s support to the Bill, saying: “Livestock worrying causes havoc up and down the country.

“The vast majority of dogs are, of course, loveable, good natured family pets and most owners, of course, are very responsible and would never dream of letting their pet chase down – never mind attack – livestock in the fields.

“However, a small minority of dogs are not kept under control, they run loose and they can aggressively chase down, attack and sometimes even kill livestock, leaving farmers to deal with the stress of their animals’ injury and death.”

Mr Reed added: “I’m very pleased indeed that (Ms Coffey) and the minister have listened to calls made at second reading and during committee stage for stronger sanctions against owners of dogs involved in livestock worrying.”

He suggested the Bill should have gone further on disqualifying offenders from owning dogs.

Speaking during the Bill’s third reading debate, environment minister Rebecca Pow said: “We know livestock worrying and attacks on livestock can have terrible impacts.”

She said a previous report highlighted 34,000 incidents of livestock worrying occur every year, adding: “Not only is it terrifying in terms of animal welfare, but it actually has a very big economic cost – it’s estimated about £2.4 million a year is lost in basically destroyed animals killed by dogs.”

Livestock worrying is already an offence through the Dogs (Protection of Livestock) Act 1953.

Measures contained in Ms Coffey’s Bill include allowing dental impressions and other relevant samples to be taken from dogs as part of evidence gathering.

Camelids – alpacas and llamas – would also be included in the definition of livestock.

The Bill received an unopposed third reading in the Commons and will undergo further scrutiny at a later date in the House of Lords.

Elsewhere in the session, Conservative MP Anna Firth (Southend West) made a renewed attempt to secure support for her Animal Welfare (Responsibility for Dog Attacks) Bill.

This would require a person in charge of a dog to take “all reasonable steps” to ensure their dog does not fatally injure another dog.

But her Bill failed to make progress as the second reading debate was still taking place when time to consider private members’ bills elapsed on Friday.