Jeremy Corbyn promised to carry on reminding voters in Conservative marginals that there “is an alternative” as he continued his election-style summer campaign with visits to two Tory-held seats on the south coast on Saturday.

The Labour leader told supporters in Southampton that Theresa May’s party should “step aside” for a Labour “government in waiting”, while he told fans in Bournemouth that there were “no no-go areas anywhere in the country” for his party.

Corbyn, who spoke for 45 minutes to dozens of supporters at a hotel in the traditional Tory stronghold, joked with supporters who peered through windows from outside – turning to them and saying: “Hello outside, I did not realise you were all out here.”

The hotel is in the constituency of Bournemouth West, which has been Conservative since its creation in 1950, but saw a 6.6% swing to Labour that cut the Tory majority almost in half in June.

Corbyn said: “We have got to reach out to everybody all over the whole country, and so this is one of many visits I am making to constituencies – particularly Tory-held marginals, which I think need to be reminded that there is an alternative and that we offer it.

“So I’ve promised I will visit all 73 of the Tory-held marginals all over the country, and I have got 35 of those planned between now and party conference in September.

“So the election was just a huge dress rehearsal for the next election.”

Corbyn spoke at length about a variety of issues including bus and train services, education, music in schools and homelessness.

He also promised he would never use personal abuse and urged Labour supporters not to either.

He said: “I understand some of our national daily newspapers are quite hostile to us … it doesn’t bother me because I don’t read it.

“They write all this stuff. I will not, and never do, respond to that stuff and I don’t use that kind of language about anybody.

“I am not getting in the gutter … we need to set an example of not using personal abuse to anybody at any time, including on social media.”

Commenting on his visit to Brussels on Thursday, Corbyn said a Labour government would have a foreign policy based on “human rights, justice, democracy and environmental sustainability”.

He said: “Ours would be a government that would be quite prepared to be very blunt with President Donald Trump, ‘Don’t walk away from the Paris climate change accord’ and stand up for the environment.”

He added of the June poll: “We were written off by every commentator and the commentariat; we were told this was an election about the re-election of Theresa May and the Tory government to be strong and stable and to beat a coalition of chaos.

“I haven’t heard too much about strong and stable since 8 June, and the only coalition of chaos I see is when I sit on our frontbench and look across the aisle.”

Following the speech, Corbyn visited the seafront, where he spoke to members of the public and posed for selfies with dozens of people who chanted and cheered his arrival and departure.

Earlier, he visited Labour’s top target seat of Southampton Itchen, which the party held from 1992 to 2015 and came within 31 votes of regaining last month.

Speaking in Guildhall Square, he said the party hopes to win Itchen at the next election “whenever it is called”, and added: “September is fine by me.”

He told the crowd: “If the Conservatives are unable to govern, they should step aside. Labour is no longer just the official opposition, we are a government in waiting.

“The Conservatives’ programme is in tatters following the public verdict at the general election. Theresa May does not have a mandate for continued cuts to our schools, hospitals, police and other vital public services, or for a race-to-the-bottom Brexit.

“Labour will fight these policies every step of the way, that make life worse for the many to maintain the privilege of the few.”

Corbyn has visited the Tory marginals of Hastings and Rye, Chingford and Woodford Green, and Hendon this month, in a bid to take the fight into Tory territory in preparation for an election which Labour strategists believe could come much earlier than the scheduled date of 2022.