The German chancellor, Angela Merkel, warned Britain not to turn its back on Europe just before heading to London on Wednesday night for a crunch meeting with the prime minister David Cameron.

Merkel is visiting the UK in the hope of resolving a growing dispute about the EU budget, with Downing Street raising the implicit threat that it could veto any increase in spending. In a speech to the European parliament in Brussels before leaving for London, the German leader issued a veiled warning that Britain would struggle alone.

"I want to have a strong UK in the EU," said Merkel in a question and answer session after her address to MEPs. "The UK was with us when we were liberated from national socialism. We still have British soldiers in Germany. I can't imagine that the UK [would] not be part of Europe.

"I think it is good also for the UK to be part of Europe. If you have a world of seven billion, and if you are alone in that world, I don't think that is good for the UK. So I will do everything to keep the UK in the EU as a good partner, and that is why I'm going to London and I will ask the inhabitants of the wonderful island to reflect that they will not be happy if they are alone in this world.

"With a strong Europe with 500 million we are in favour of freedom of speech, freedom of expression, freedom of religion and democracy. Look around the world at where this isn't the case and be happy that we are together".

The meeting at No 10 is part of a series of bilateral talks before a gathering of all 27 EU member state leaders on 22 November.

Before Merkel and Cameron sat down to discuss the thorny issue of the EU budget for 2014-20 over dinner at No 10, the prime minister said they were "both believers that European countries have to live within their means, as well as the EU".

Asked whether he would be urging his German counterpart to support a cut or a freeze in the EU budget, he said: "I believe it would be wrong for the European budget to increase at a time when we are having to make difficult decisions not just in Britain but all over the European Union to get our budgets back to balancing. That's why I've said it should be at best a cut, at worst a freeze.

"Whatever the discussions we have today I will be trying to get a good deal for the British taxpayer, a good deal for Britain, one that I can put before the British Parliament, one that I can put before the British people."

Merkel said European leaders always had to "do something that will stand up to public opinion back home". She said: "Not all of the expenditure that has been earmarked has been used with great efficiency … We need to address that."

But pressed as to whether she would support a budget freeze, she added: "I beg leave to first discuss this with the prime minister. What is in my interests is that we use our money effectively."

Britain is demanding a "real-terms" freeze in the budget, which would be set at 2011 levels increased only for inflation. MPs voted last week to go further and demand a real-terms cut in spending by the EU.

The European commission has suggested a 5% increase in spending, and Germany, supported by Ireland, is in favour of spending 1% of GDP, suggesting the budget would rise further as European economies grow.

If there is no agreement, the default position is that the 2013 budget will be rolled over to future years, with an increase for inflation added – a move Westminster would not have any power to reject.

Cameron said on Wednesday that he "never had particularly high hopes" of an agreement this month. "You have 27 people around the table with 27 different opinions but I am very clear I am not going to agree to a future financial framework that isn't in Britain's interests," he said.

The prime minister earlier said the commission's proposed budget increase amounted to €100bn (£80bn) and was "completely ludicrous" .

"I want to make a very strong argument to the commission: how can they argue that countries should be cutting spending and taking tough decisions if they are not prepared to take tough decisions themselves?"

The Centre for European Reform has calculated the UK contribution would be £7.4bn a year if the budget were frozen, while the German or commission plans would result in an additional £400m-550m a year "at most". John Springford, the CER's research fellow, said: "If Cameron brought down the negotiations over such a small sum, the UK would find itself pressed further into the margins of Europe. It would do better to compromise on the overall size of the budget and negotiate for it to be spent more wisely."

Although Germany wants Britain to stay in the EU, as one of the biggest net contributors of funds and as part of a counterbalance to the powerful Franco-Mediterranean alliance, Merkel is said to have indicated privately that she would not fight hard against any planned exit.

Merkel used her speech in Brussels to call for the surrender of national powers over tax-and-spend policies to Brussels by the 17 countries in the eurozone within three years, in order to rescue and shore up the embattled single currency.

The German leader voiced Berlin's determination to stand by the euro and to strengthen the EU through greater integration of policy-making. But her commitment came with a price tag many in the eurozone may find hard to swallow. Merkel called for a major centralisation in Brussels of sovereign national powers in fiscal, budgetary, and economic policies, arguing that action already taken during three years of the euro crisis had only left the job half-done.

"Stronger economic policy co-ordination will also perhaps be needed in areas that affect the core of national sovereignty. I'm thinking of sensitive policy areas such as labour market and tax policy," she said. "We need solutions creating a sensible balance between the necessary new intervention rights at the European level and the scope for action of the member states and their parliaments. The European institutions must be strengthened to allow them to correct mistakes and breaches of the rules effectively."

• This article was amended on 8 November 2012. The name of the CER's research fellow was corrected.