The FTSE-100 Index climbed 56.7 points to 6487.2, following a 1.5% gain on Thursday, and on Wall Street the Dow Jones Industrial Average started trading on the front foot after prior session saw its best performance in nearly two years.
Investors took heart after it emerged Republicans are considering a short-term increase in the debt ceiling to avoid a US default.
The ongoing stock rally came as nearly 700,000 small investors in the UK cheered a big opening day rise for shares in Royal Mail.
The developments in the United States, with the government potentially getting six more weeks to come to a longer term agreement, was welcomed after several days of turbulence.
Alpari market analyst Craig Erlam said: "It's still not clear whether the Republicans will want anything in return, which could scupper a deal being done, but at least it's progress."
The pound struggled on the currency markets after disappointing construction figures, which showed output from the sector dipped by 0.1% month-on-month in August. That left a pound worth 1.59 dollars and 1.18 euros.
Leisure group Whitbread was near the top of the FTSE-100 risers board as an upgrade from Citigroup added to speculation over the potential for a break-up of the Costa coffee and Premier Inn hotels chain. Shares rose sharply and were up another 96p to 3210p today.
Other risers included Standard Life, which climbed 9.1p to 355.5p, while Lloyds Banking Group added 1.1p to 76p after it sold its Australian operations to Westpac in a deal worth £900 million.
In a strong session for financial stocks, Barclays rose 3.5p to 278p, HSBC lifted 11.3p to 689.6p and Aberdeen Asset Management added 10p to 393.4p.
Royal Mail shares, which were priced at 330p by the Government, surged by more than a third to 455p in conditional dealings ahead of the formal launch on Tuesday. The rise meant 690,000 ordinary investors who have bought around £750 worth of stock gained more than £280 each.
Elsewhere, shares in defence group Chemring slid by more than 20% as it followed the lead of BAE Systems yesterday in highlighting the impact of the US government shutdown on its business. It warned that this and other factors would cause operating profits to be £8 million lower than hoped for in the current financial year, leaving shares 64.4p lower at 220p.
The biggest risers on the FTSE -100 were Travis Perkins up 53p to 1678p, Whitbread 96p higher to 3210p, Glenccore Xstrata 9.3p ahead to 335.9p and Diageo 52p higher to 1973p.
The biggest fallers were Croda International down 125p to 2477p, BAE Systems 14.4p lower to 436.3p, Royal Bank of Scotland down 8p to 376.9p and Wolseley down 32p to 3169p.