Labour shadow immigration minister Chris Bryant has been contorting all over the shop in the last two days, as he backtracked and side-stepped his way around a speech on immigration. And by all over the shop, I mean two shops in particular: Tesco and Next, who were reportedly the original targets of his criticism of employers who favour cheaper migrant workers over the home-grown variety.

Sections of the speech were sent to The Sunday Telegraph, which may or may not have conflated two sections – Bryant insisted on the Today programme there was no one to blame but himself, but in a way that suggested someone at The Telegraph was getting a very serious ticking off from Labour’s press office.

The problem was, Bryant’s speech had got some significant facts wrong – such as siting a former Tesco distribution centre in Kent when it was actually in Harlow, Essex. His claims were also flatly refuted by Tesco and Next, sparking much backpedalling from Bryant – including the bizarre spectacle of him clarifying what he hadn’t yet said in a speech he hadn’t yet given.

Tesco has played this situation with a commendably straight bat – its flat-out denial of Bryant’s claims led to the insertion of a line in his hastily modified speech yesterday in which he recognised it was “a good employer and an important source of jobs in Britain” (Tesco then sweetly thanked him for acknowledging this).

Tesco’s UK operations director Gerry Gray then published a detailed blog on Monday afternoon outlining its approach to recruitment, insisting that when it moved staff from Harlow to a new centre in Dagenham, it did not offer them a pay cut. This was accompanied by the company’s recruitment charter for Dagenham, drawn up in April, which includes the promise it would not recruit staff from outside the UK “until such time that the quality or quantity of local labour has been exhausted”.

There are a number of lessons here. For Chris Bryant, it highlights the risks of pre-briefing newspapers and not checking your facts. For Labour, it’s a reminder immigration remains a dauntingly difficult subject – one that can easily burn your fingers. And more generally, it shows the perils faced by politicians in tangling with the UK’s biggest retailer. Labour’s shadow business secretary Chuka Umunna walked a similar tightrope recently when he complained about the Tesco Express stores saturating Streatham High Road in his constituency. He can’t be too critical, however, if he wants to be business secretary one day – and maintain a healthy relationship with a company that employs 330,000 people in the UK. Rather like Bryant, he had to concede, vaguely, that Tesco was “doing good things”.

Tesco, meanwhile, may have won this round, but it – and its rivals – can’t afford to be complacent. Harlow’s Conservative MP Robert Halfon remains a stern critic of Tesco’s behaviour in his constituency and has posed questions about the types of workers employed at its Dagenham DC and their wages. There’s nothing “un-Conservative” in criticising Tesco, he says. Chris Bryant may be grateful for this bit of unexpected support. Or he may be wishing he’d never brought the whole thing up.