Have you ever stared down at a pound bill and wondered why it has value? Why does a worthless piece of paper have value?
Is it because you can exchange it for gold? This was true until the 1970s, where there was something called the Bretton Woods System, where you could convert other currencies into the US Dollar which could be converted to gold. Some people would say it has value because others think it does. If we all have faith in the currency, it has value. And this is partially true - look at bitcoin for example. Money also has value as legal tender, the only way to pay debts.
But what is the main reason currencies have value. It is surprising. The main reason is taxation. Taxes require people to find money to pay for them. Otherwise, they go to jail. This is not the only thing needed though - governments need to carefully manage their currency and not print too much or it will cause inflation, and there has to be proper enforcement.
This is the real reason for taxation - not to "fund" spending. Where will the money come from? The taxes come first, then when there is demand for the currency, the government spends money on stuff - infrastructure, public sector workers, social programs, etcetera...
Let's take a teacher's wage for example. The teacher pays some income tax and NI on the money. The teacher pays some Council Tax. The teacher will save and spend money. When the money is spent, it attracts VAT. The money goes to a corporation and they pay wages and corporation tax. It is invested, attracts capital gains tax, etcetera... The point is money is a flow.
The only money that the government does not get back as tax is saved. In a closed economy, this is what is meant by the "deficit." The deficit is the private sector's surplus. As long as the government is a currency issuer, there is low default risk (the government could go mad and default) Of course you need to include the external sector (foreigners) and the banking system.
With a foreign sector, a government running a trade surplus (imports less than exports) can run surpluses while a trade deficit nation can't without private sector deficit (going deeper into debt.) You also need to take into foreign investments, foreign aid, remittances, etc to get a current account surplus or deficit.
Banks can create money. Say you borrow £100,000 from a bank. The bank enters it as a "deposit" in your account (a promise to pay money.) Although it does not create any money, the bank's credit money is accepted by most (i.e. non cash only) stores. These Bank IOUs are treated like real money. When you pay back the loan, the money is destroyed.
You get an equation:
Private deficit + Public Sector Deficit + Rest of World Deficit = 0
So for a country with a trade deficit like the UK it is a silly idea to aim for a budget surplus.