Be aware that using real soap, which some of these that have been mentioned are, including Friendly Soap and Funky Soap, is very bad for your hair (and skin) long term, even using a vinegar rinse. Real soap opens up the cuticles on the hair shaft and roughs them up as it is strongly alkaline. Using an acid rinse of some sort neutralises the soap to an extent, but the damage has been done by this point. Eventually, the roughness builds up and causes real damage. Yes, I know people used soap as shampoo for centuries, but they tended not to wash as frequently as people do nowadays.
I looked at a lot of information when I was trying to make my own properly formulated personal care products (for personal use only, I've never sought to sell anything) and a lot of the claims for soap shampoo bars are not scientifically supported. Obviously they're better for the environment than plastic containers though.
You're best looking for what's known as syndet shampoo bars, which are synthetic detergent, and are much closer to the PH of your skin and hair. I'd personally avoid ones with SLS and SLES, which I believe a lot of the LUSH bars are and go for ones using SCI (sodium cocoyl isothionate) and cocamidopropyl betaine, which are extremely gentle. These are detergents made from natural sources such coconut, whereas others can be derivatives of petroleum. It's worth checking the ingredients list on the product; real, saponified soap will have on ingredients listed as '...ate', such as this Friendly Soap ingredients list: 'Sodium cocoate, Sodium olivate, Sodium castorate, Aqua, Lavandula angustifolia (lavender) essential oil contains linalool, limonene, geraniol, Pelargonium graveolens (rose geranium) essential oil contains geraniol, citronella, linalool'
I've made my own shampoo bars based on SCI and cocamidopropyl betaine and they're not bad at all, though I have to say these detergents are a bugger to track down and aren't that cheap because of postage costs.
On the other hand, I don't always practise what I preach, because I buy lovely goats' milk soap from an eBay seller that my skin bloody loves 
I hope this essay has helped someone make a decision and hasn't come across as too patronising or preachy, which I suspect it might be a bit, sorry if has.