A council in the north-east of England has been labelled “laughable, ludicrous and short-sighted” after it attempted to force a family-run sci-fi museum to destroy a Doctor Who Dalek shelter because it did not have planning permission.

Neil Cole, an art teacher, is embroiled in a planning row over the latest addition at his Museum of Classic Sci-Fi, which he founded last October in the cellar of his Grade II-listed, Georgian townhouse in Allendale, Northumberland.

The Doctor Who superfan built a replica of a Dalek, the feared cyborg in the TV series, with the help of local schoolchildren, and installed it outside his house as an extraterrestrial guard and selfie magnet.

To keep the Dalek dry, Cole built it a little wooden shed, raising the hackles of Northumberland county council’s planning overlords, who said it was out of keeping with his period property.

In January, they told him he would have to take it down unless he applied for retrospective planning permission.

Cole put in an application last week and has been supported by dozens of sci-fi fans from around the UK, who have written letters of admonishment to the council.

“That Northumberland county council has taken exception in the first place is one of the most laughable, ludicrous and shortsighted viewpoints I have ever heard from a council,” wrote Simon Horton, from Walsall.

“Indeed, given the ludicrous nature of the complaint, this entire issue smacks of mere pettiness and vindictiveness on the part of whoever has brought the complaint, and is the kind of bombastic, high-handed stupidity that gives councils a bad name.”

Martin Bulmer, from Coalville, in Leicestershire, said the council should recognise the value of the museum in attracting tourists instead of threatening it with planning law. “I may never have heard of Allendale without it, and would not otherwise have brought five adults to the area for a week’s holiday,” he wrote.

Cole said he hoped the council would take heed: “If it hadn’t been for the amazing local support we probably would’ve packed up by now. Hopefully the council will see how loved it is – I’ve just gone out on a limb and tried to create something unique,” he said.

“Before we moved in the house was in an awful state, there was a horrible old caravan outside, and that wasn’t a problem, but this is?”

Supporters have until 6 June to respond to the consultation.