No. Precisely because regardless of £0.99 or $0.99 or whatever sales, pennies are needed, purely to serve as base units. Without a base unit, mathematically speaking, you're going to be screwed when it comes to adding or subtracting values. There's no feasible way of standardising prices everywhere so that every single transaction will result in more than a single penny difference between other currency values, meaning that when dealing with multiple transactions you are pretty damn likely to need a penny somewhere down the line. This doesn't just apply to single penny difference either. In the UK the next size denomination is 2p, then 5p, then 10p. In the US, isn't it straight up to 5 cents, then 10 cents? You'll thus have the same problem when dealing with 2p, 3p, 4p, etc. differences.
Simply put, base units are essential, and thus getting rid of the penny would cause more problems than it solves.