Titchmarsh isn't my kind of gardener at all, and as others have pointed out, has a vested interest in promoted highly cultivated, high maintenance gardens. His whole approach is really dated. Give me Monty Don any day of the week.
Research shows that the best gardens for wildlife have a mix of habitats and different types of planting. (My parents are keen gardeners and my dad worked most of his life in conservation and environmental protection, so they've done tons of research and learning about this.)
People have different notions about what 'rewilding' means. Literally just letting your garden go to waist-high grass and brambles is certainly better than plastic grass, paving, no plants and a patio heater - but isn't actually that great for biodiversity (and also means that your garden becomes a space that you can't actually use to sit and relax and engage with nature in).
However, a manicured lawn, only planting annuals every year that you just grow and throw away, killing off all the daisies and clover in your lawn, using pesticides and weedkillers, over-pruning, growing plants that need feeding or aren't right for your soil type or climate, and throwing peat-based compost and chemical fertilisers down all the time isn't good either.
Planting a good mix of low maintenance, hardy flowering plants that don't need huge amounts of water and don't need soil pH adjustments, leaving seed-heads up over winter instead of dead-heading/cutting back, having a range of different, insect-attracting plants/shrubs for pollinators, and letting things like clover, dandelions and buttercups grow in your lawn instead digging them up and mowing every week, is usually great for wildlife. If you've got the space, a wild corner where you let some nettles and stuff grow and have a pile of old logs is good, as is a nature pond (so a natural pond with native water plants, untreated water and no goldfish). Basically you want a nice mix of habitats and minimal intervention/watering, no pesticides, slug pellets or artificial weedkillers, but equally you need to keep an eye on things to make sure that one plant isn't taking over everything else and that you've still got a nice variety going on.