Midfielder Clifford penned a two-year deal and defender Bennett has signed a one-year contract after successful trials at Roots Hall.
They took the number of new arrivals at the club to six and Brown is happy with how things are looking ahead of the curtain-raising clash with Plymouth Argyle.
Brown told the club's official website: "I'm very pleased to have Conor and Julian both on board, they've really impressed me during their trial and to have them here ahead of the start of the season is great.
"We identified positions we needed to improve and both of the lads have done really well and shown they are ready to fill the spots available.
"Conor is a midfielder who likes to rough it up a bit and I think we were missing that, while Julian has plenty of experience in winning promotion and I'm sure that will help us this season."