The Port of London had excellent facilities for most ships but the Thames just wasn't deep enough for these 32,000 tonne liners such as the Lusitania and Mauritania, before we even begin to take the "Olympic class" into consideration.
The Thames was still one of Europe and the worlds major shipping ports regardless. You'd find "back in the day" many fine ships of the Union-Castle Line, the Peninsular & Oriental Steam Nav. and the British-India Steam Nav. docked in the Port of London, to say nothing of many smaller shipping lines.
Don't forget our dear old River Clyde ! We could give Southampton and Liverpool a run for their money too !
Decades ago, Glasgow, Port Glasgow and Greenock also handled a huge amount of cargo, mail and passengers going in and out of the UK. The Canadian -Pacific Line and the Anchor Line had a particularly strong presence here on the Clyde. All gone now sadly although some big cruise ships still use Greenock as a port of call.