Alexander, who was much criticised for his low profile, was moved to the Cabinet Office following the Government reshuffle yesterday after the resignation of Transport Minister Stephen Byers.
Timms worked for 15 years in the IT and telecommunications industry, first for Logica and then for analyst group Ovum, before his election.
David Roberts, chief executive of the IT directors' organisation the Infrastructure Forum (Tif), whose members represent more than 100 leading blue-chip UK businesses, demanded action from the new minister.
"A quick measure of the new minister will be what he does to stimulate the uptake of broadband," said Roberts. "The very large companies that are the principal members of Tif are not directly affected but the smaller businesses that make up their supply chain, product development, sales and distribution channels have been throttled," he said.
Roger Till, a director, of the e-commerce lobbying organisation e-centre, said: "We need a Minister who can take a clear strategic view of e-commerce and bring some sense to the rather piecemeal approach coming from the European Commission."
Sally Low, senior policy advisor for e-commerce at the British Chambers of Commerce (BCC), said Timms had a lot to do to realise Tony Blair's aim of making Britain the best place in the world for e-business.
The BCC wants the Government to get the physical and political infrastructure right for e-commerce, said Low. That means driving up broadband uptake. In addition she called on government to "tackle the barriers to the uptake of e-commerce, including getting the right regulatory framework, take measures to encourage investment and give businesses access to the skills and advice they need".