From April, inheritance tax will only be levied on the value of an estate above the allowance of pounds 231,000, which has been raised by pounds 8,000.
Capital gains tax will only be levied on amounts exceeding pounds 7,100 - a pounds 300 rise over last year. There will be no change in the rate of either tax.
Mr Brown said that Britain now had the lowest rate of capital gains tax in its history. He added that only 97 per cent of inherited estates would be liable to inheritance tax.
The moves relieved tax advisers, who had feared a full-blooded crackdown on inheritance tax. Accountants and tax planners feared the Budget would include measures to block the most common loophole in the tax, relied upon by tens of thousands of people to exempt their inherited estates.
The loophole, known as the "potentially exempt transfer", involves transferring wealth to a trust in the name of dependents at least seven years before the person transferring it dies. It is partly because of this loophole that inheritance tax barely raises pounds 1.8bn a year.
The Chancellor instead announced a smaller crackdown, buried in the fine print of the Budget, on some of the more exotic avoidance techniques used by the wealthiest investors.
Chas Ray-Chowdrey of the Association of Chartered Certified Accountants said: "We are pleased that there was no crackdown on the transfers. But the overall bad news is in the underlying details not announced in the Budget speech."
In particular, the Budget will block a loophole made famous by Lady Ingram, an elderly relative of "It-Girl" Tara Palmer-Tomkinson. Earlier this year Lady Ingram won a legal battle with the Revenue that went all the way to the House of Lords.
Lady Ingram had gifted property worth millions of pounds to her solicitor, who arranged a lease-back to her so she could still live in it. The freehold of the property was then passed to dependents, taking it out of her taxable estate.
The avoidance technique is based on the principle of "gifting" a property while retaining the right to live in it. In Lady Ingram's case she also retained the right to a rental income.
The Revenue regarded this technique as abusing the proper notion of a gift - calling it a "gift with reservation" - and pursued her to the House of Lords. The Lords ruled in her favour.
Yesterday's measures were designed to redress the legal balance in favour of the Inland Revenue so "gifts with reservation" can be taxed. Officials view the Lords' decision as showing the rules do not work as they should. The new measures will stop avoidance where a donor keeps a financial interest in the property and has the right to live on it.
Responding to the changes on capital gains tax, the tax industry welcomed the Budget but said it was not enough to make up for the complexities introduced in the last Budget.
Last year, Mr Brown stopped the use of an inflation index to offset capital gains tax, instead bringing in a tapered tax which reduces to 10p on assets held for 10 years or more. Tax advisers say the move has made the tax more complex to administer.
Angela Knight, a former Treasury minister who heads the Association of Private Client Investment Managers, said: "A number of small investors will still be liable to pay. At minimal cost the Chancellor could have cut them out of CGT altogether."