You'd be hard pressed to find a more left-wing "center-left" party than Labour currently. Even during Blair they were well to the LPC's left.
Certainly on fiscal issues, Martin and Chretien were definitely more conservative than Blair was. On social issues perhaps more left wing as they legalized gay marriage which Blair didn't, mind you Blair said he regretted he hadn't done this and also the courts forced Martin and Chretien's hand, doubt they would have done it if the courts hadn't ruled on it. A lot of people place Blair to the right because he went into Iraq which Chretien opposed, but that is one issue and you cannot place someone on the spectrum on one issue. On that issue Blair was more in line with right wing than left wing parties, but on most other issues not so much. Perhaps on fiscal issues Trudeau is more left wing as he raised taxes on the rich, something Blair never did although Brown did (He raised top rate from 40% to 50% while Trudeau raised Canada's top rate from 29% to 33% but since we have provincial unlike the UK our combined rate was mid to high 40s before Trudeau while now low 50s in most provinces and high 40s in a few so comparable). But when compared to Corbyn, he is well to the left of any Liberal leader and in fact even to the left of the NDP.
He wants free tuition which no party in Canada is calling for. On corporate taxes he wants to raise it back to 26% which is close to what Canada is now, while on income taxes he wants to hike the top rate from 45% to 50% and if you take the combined provincial + federal rate, we were around 45% depending on province under Harper while around 50% now. Mind you his shadow chancellor John McDonnell wants to raise top rates to 60% and no party not even the NDP is calling for rates that high. Also too Britain only has federal rates while Canada has federal + Provincial and I suspect the reason for a high top rates is that they are separate and many leaders in both ignore that and just look at their own jurisdiction. If we had only federal taxes, I highly doubt even the NDP would push the top rate over 50%, that is more a result of the fact we are a decentralized federation as opposed to unitary state.
But on nationalization, only Niki Ashton in the NDP went down this route. True water and postal service are public in Canada unlike the UK, but there's a big difference between wanting to stop privatization of something and then reversing it once done. On utilities, they are public in many provinces but Trudeau's closest ally Kathleen Wynne in Ontario just sold off over 50% of the shares for Hydro One which is the electric utility in Ontario so exact opposite of Corbyn. Likewise in Nova Scotia and Alberta, you had/have NDP governments and electricity is private in both provinces yet neither tried to bring it back into public ownership. On rail, we still have VIA Rail, but tracks and freight are private and were privatized by the Liberals back in 1995 and no party has talked about re-nationalizing it. That being said somewhat comparing apples to oranges as rail in Canada is mostly freight while in UK mostly passenger and EU rules don't allow track ownership for companies that operate on it whereas in Canada usually the company that owns the tracks runs the trains on it (although VIA Rail doesn't own any tracks, instead they use CN and CP Rail and have to pay fees to use them).