Speaking at the Battersea Arts Centre in South London, Ms Swinson commented on the party’s previous coalition with the Tories and reiterated her desire to stop Brexit by revoking Article 50.
Both the Conservatives and Labour have suggested the choice for PM is between their respective leaders, Ms Swinson has strongly insisted she is also a contender in getting the keys for Number 10.
Continuing her preparations ahead of the December 12 general election, she told the crowd: “So while I look at what is on offer from Boris Johnson and Jeremy Corbyn, I know I could do a better job than them as prime minister.”
She said the Lib Dems had better policies than what was on offer from “the tired two old parties led by men who want to rehash ideas from the past” and added: “Whether its the 1870s or the 1970s.”
Ms Swinson also shared her desire to “bring the country together”, criticising former PM Theresa May for having “failed to do so”.
When asked how she would plan to unite Remain and Leave voters after “stopping Brexit”, she said: “It’s very important to bring the country together. I think that’s something that Theresa May failed to do when she became prime minister.
“And, of course, there are many things that people are united by. If you look at the childcare policy that we’ve outlined today. You know, there’s parents who voted Remain or voted Leave will find this something that’s attractive.
“Similarly when it comes to mental health, we’re tackling the climate emergency, our ambitious plan for the future is about facing forward and how we can take the whole United Kingdom forward together.
“Four nations in our wonderful family of nations stronger together in the European Union and focusing government on making people’s lives better.”
Following he speech, Ms Swinson also reflected on her previous time in government.
She said: “I think that time in government is something where we did achieve many many good things and implement lots of Lib Dem policies from shared parental leave to same-sex marriage to more money for poorest pupils in schools through the pupil premium.
“But we didn’t get everything right and we’ve learned from that.”
She said her party should have stood against the bedroom tax and said it “got it wrong” on tuition fees.
At the rally, Ms Swinson also announced that working parents could receive 35 hours of free childcare per week when their baby reaches nine months under Liberal Democrat plans.
Speaking from the rally, she said: “The choice for parents is simply not good enough. For so many people the cost of childcare means returning to work is impossible.
“How many of us know friends, usually women, who faced with astronomical childcare fees decide to stay at home instead of going back to their career? Maybe taking a couple of years out until the current free provision starts.”
She said the proposal would close the gap between the end of paid parental leave and the start of free childcare provision.
Additional reporting by PA.